id
stringlengths 39
39
| setting_key
stringclasses 1
value | setting_name
stringclasses 1
value | messages
listlengths 1
1
| ground_truth
stringclasses 167
values | dataset
stringclasses 1
value |
|---|---|---|---|---|---|
comp_parametric_intersection_train_0900
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 1, q: 2, k: 1, g: 2}, shuffle the letters in the word, what is the probability of no letter 'q' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
23
|
math
|
comp_parametric_intersection_train_0901
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 1, a: 4, k: 1, f: 2}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15
|
math
|
comp_parametric_intersection_train_0902
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 4, l: 4}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
89
|
math
|
comp_parametric_intersection_train_0903
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {e: 2, l: 2, r: 4}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12
|
math
|
comp_parametric_intersection_train_0904
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 2, z: 6}, shuffle the letters in the word, what is the probability of no letter 'x' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12
|
math
|
comp_parametric_intersection_train_0905
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 3, b: 3, w: 2}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12
|
math
|
comp_parametric_intersection_train_0906
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 2, q: 2, s: 4}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
47
|
math
|
comp_parametric_intersection_train_0907
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 5, i: 1}, shuffle the letters in the word, what is the probability of no letter 'i' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0908
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 1, r: 3, w: 2}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0909
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 3, g: 4}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
51
|
math
|
comp_parametric_intersection_train_0910
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {c: 1, l: 2, r: 2, d: 3}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15
|
math
|
comp_parametric_intersection_train_0911
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 3, u: 3}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0912
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 3, l: 3}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0913
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 4, l: 2}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
16
|
math
|
comp_parametric_intersection_train_0914
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 4, j: 2}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0915
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {c: 5, a: 2}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
22
|
math
|
comp_parametric_intersection_train_0916
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {u: 2, i: 2, s: 2}, shuffle the letters in the word, what is the probability of no letter 'i' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0917
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {n: 4, b: 3}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
48
|
math
|
comp_parametric_intersection_train_0918
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 2, m: 4, d: 1}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
34
|
math
|
comp_parametric_intersection_train_0919
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 4, j: 4}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
89
|
math
|
comp_parametric_intersection_train_0920
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 2, u: 3, d: 1, v: 1}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0921
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 2, z: 3, g: 2}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0922
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 2, d: 1, j: 2, f: 2}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0923
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {u: 5, j: 2}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
22
|
math
|
comp_parametric_intersection_train_0924
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 2, m: 3, d: 3}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
41
|
math
|
comp_parametric_intersection_train_0925
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 3, t: 1, g: 3}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
48
|
math
|
comp_parametric_intersection_train_0926
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 3, v: 3}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0927
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {t: 2, a: 3, x: 2}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
34
|
math
|
comp_parametric_intersection_train_0928
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 3, l: 5}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
41
|
math
|
comp_parametric_intersection_train_0929
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {u: 2, h: 3, r: 2}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
34
|
math
|
comp_parametric_intersection_train_0930
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {j: 2, d: 2, s: 2, w: 2}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12
|
math
|
comp_parametric_intersection_train_0931
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 2, s: 2, h: 2, r: 2}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
47
|
math
|
comp_parametric_intersection_train_0932
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 1, d: 2, u: 1, s: 3}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0933
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 2, v: 2, j: 2}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0934
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {d: 4, c: 4}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
89
|
math
|
comp_parametric_intersection_train_0935
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 2, x: 1, y: 1, l: 2}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0936
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 2, k: 1, u: 3}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0937
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 2, s: 3, p: 1, n: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
48
|
math
|
comp_parametric_intersection_train_0938
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 1, f: 2, h: 2, b: 1}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0939
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 1, u: 4, v: 1}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0940
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 2, l: 2, z: 1, x: 1}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0941
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 3, g: 3, x: 2}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
41
|
math
|
comp_parametric_intersection_train_0942
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 2, z: 3, n: 2, c: 1}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
47
|
math
|
comp_parametric_intersection_train_0943
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 2, u: 2, v: 1, q: 1}, shuffle the letters in the word, what is the probability of no letter 'q' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0944
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 3, d: 3}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0945
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 2, x: 1, l: 1, e: 2}, shuffle the letters in the word, what is the probability of no letter 'x' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0946
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 3, f: 1, g: 1, k: 2}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0947
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 4, a: 4}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
19
|
math
|
comp_parametric_intersection_train_0948
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 2, o: 2, r: 2}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
23
|
math
|
comp_parametric_intersection_train_0949
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 2, a: 1, l: 1, h: 3}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0950
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 2, q: 5}, shuffle the letters in the word, what is the probability of no letter 'q' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
22
|
math
|
comp_parametric_intersection_train_0951
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 2, f: 1, t: 1, b: 4}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15
|
math
|
comp_parametric_intersection_train_0952
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 2, t: 3, m: 1, r: 2}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
47
|
math
|
comp_parametric_intersection_train_0953
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 5, k: 3}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
67
|
math
|
comp_parametric_intersection_train_0954
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {d: 2, o: 3, l: 2, s: 1}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
47
|
math
|
comp_parametric_intersection_train_0955
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 6, p: 2}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12
|
math
|
comp_parametric_intersection_train_0956
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {c: 3, n: 2, i: 1}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
23
|
math
|
comp_parametric_intersection_train_0957
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 2, r: 1, v: 2, s: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0958
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {d: 1, z: 2, m: 1, k: 2}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
23
|
math
|
comp_parametric_intersection_train_0959
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {j: 4, v: 2}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
17
|
math
|
comp_parametric_intersection_train_0960
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {a: 4, t: 2}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
23
|
math
|
comp_parametric_intersection_train_0961
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {u: 5, f: 3}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
67
|
math
|
comp_parametric_intersection_train_0962
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 5, p: 3}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
67
|
math
|
comp_parametric_intersection_train_0963
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 1, a: 2, b: 3}, shuffle the letters in the word, what is the probability of no letter 'a' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
23
|
math
|
comp_parametric_intersection_train_0964
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 1, m: 3, e: 3}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0965
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 4, p: 1, g: 1, q: 2}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15
|
math
|
comp_parametric_intersection_train_0966
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 1, f: 2, e: 4}, shuffle the letters in the word, what is the probability of no letter 'e' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
41
|
math
|
comp_parametric_intersection_train_0967
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 4, k: 3}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
48
|
math
|
comp_parametric_intersection_train_0968
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {t: 3, v: 1, k: 1, e: 2}, shuffle the letters in the word, what is the probability of no letter 'e' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
34
|
math
|
comp_parametric_intersection_train_0969
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {t: 1, b: 2, w: 1, g: 2}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
23
|
math
|
comp_parametric_intersection_train_0970
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 5, t: 3}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
67
|
math
|
comp_parametric_intersection_train_0971
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 5, d: 1}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0972
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 3, i: 4}, shuffle the letters in the word, what is the probability of no letter 'i' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
41
|
math
|
comp_parametric_intersection_train_0973
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 4, l: 1, t: 2}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0974
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {c: 5, q: 2}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
22
|
math
|
comp_parametric_intersection_train_0975
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 2, p: 1, f: 1, w: 2}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0976
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 2, i: 2, g: 1, n: 3}, shuffle the letters in the word, what is the probability of no letter 'i' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
47
|
math
|
comp_parametric_intersection_train_0977
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 1, o: 2, l: 2, x: 1}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0978
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 2, f: 2, k: 2, j: 2}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12
|
math
|
comp_parametric_intersection_train_0979
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 2, d: 2, e: 4}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
47
|
math
|
comp_parametric_intersection_train_0980
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 3, d: 2, u: 2}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
34
|
math
|
comp_parametric_intersection_train_0981
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 5, y: 3}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
41
|
math
|
comp_parametric_intersection_train_0982
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 2, c: 2, u: 1, v: 1}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0983
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 6, o: 2}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15
|
math
|
comp_parametric_intersection_train_0984
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 2, m: 3, o: 2, d: 1}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15
|
math
|
comp_parametric_intersection_train_0985
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {a: 3, p: 2, h: 2}, shuffle the letters in the word, what is the probability of no letter 'a' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
48
|
math
|
comp_parametric_intersection_train_0986
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 2, j: 2, u: 3}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0987
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 2, f: 1, n: 2, z: 3}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
41
|
math
|
comp_parametric_intersection_train_0988
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {x: 3, v: 3, k: 2}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
41
|
math
|
comp_parametric_intersection_train_0989
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 3, w: 3}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
27
|
math
|
comp_parametric_intersection_train_0990
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, s: 2, l: 4}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12
|
math
|
comp_parametric_intersection_train_0991
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 1, i: 3, k: 3}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0992
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {l: 3, f: 3, r: 1}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0993
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 2, s: 4, y: 2}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12
|
math
|
comp_parametric_intersection_train_0994
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 2, e: 2, y: 1, r: 2}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
34
|
math
|
comp_parametric_intersection_train_0995
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 2, c: 2, r: 3}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
34
|
math
|
comp_parametric_intersection_train_0996
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 2, b: 4, j: 1, v: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12
|
math
|
comp_parametric_intersection_train_0997
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 3, h: 2, a: 1}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0998
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 2, a: 3, d: 3}, shuffle the letters in the word, what is the probability of no letter 'a' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
41
|
math
|
comp_parametric_intersection_train_0999
|
comp_parametric_intersection
|
Combinatorics (Probability) + Algebra (Function Intersection)
|
[
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 1, c: 4, t: 3}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
19
|
math
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.