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_0300
|
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 2 letters from the multiset {m: 3, c: 1, h: 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}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0301
|
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: 4, k: 2}, 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_0302
|
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 2 letters from the multiset {p: 2, y: 1, e: 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}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0303
|
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, p: 3, h: 1, e: 1}, 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}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0304
|
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 2 letters from the multiset {c: 3, y: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0305
|
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: 4, f: 3}, 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}"
}
] |
44
|
math
|
comp_parametric_intersection_train_0306
|
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 2 letters from the multiset {s: 1, k: 1, n: 1, o: 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}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0307
|
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: 1, r: 2, q: 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0308
|
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 {o: 1, l: 3, r: 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}"
}
] |
51
|
math
|
comp_parametric_intersection_train_0309
|
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, p: 3, g: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0310
|
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: 1, h: 3, y: 2, 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_0311
|
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 2 letters from the multiset {n: 3, d: 2, s: 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_0312
|
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 2 letters from the multiset {p: 3, v: 4}, 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}"
}
] |
10
|
math
|
comp_parametric_intersection_train_0313
|
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 2 letters from the multiset {w: 1, u: 1, e: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0314
|
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 {t: 2, o: 2, a: 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}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0315
|
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, n: 1, m: 1, u: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0316
|
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 2 letters from the multiset {e: 1, i: 1, m: 1, b: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0317
|
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 2 letters from the multiset {y: 2, i: 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0318
|
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 2 letters from the multiset {r: 1, i: 1, e: 1, x: 1}, 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0319
|
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 {a: 2, n: 2, r: 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}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0320
|
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 2 letters from the multiset {x: 3, l: 4}, 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_0321
|
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 2 letters from the multiset {i: 3, q: 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}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0322
|
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, q: 1, c: 1, v: 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}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0323
|
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 2 letters from the multiset {w: 1, q: 3, z: 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}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0324
|
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 2 letters from the multiset {f: 2, c: 2, y: 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}"
}
] |
12
|
math
|
comp_parametric_intersection_train_0325
|
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: 1, z: 4, x: 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}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0326
|
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 2 letters from the multiset {o: 2, k: 3, 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}"
}
] |
12
|
math
|
comp_parametric_intersection_train_0327
|
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 2 letters from the multiset {n: 3, u: 1, l: 2, s: 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}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0328
|
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: 1, s: 2, u: 1, z: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0329
|
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, y: 2}, 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}"
}
] |
4
|
math
|
comp_parametric_intersection_train_0330
|
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 2 letters from the multiset {s: 2, d: 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0331
|
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: 5, n: 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}"
}
] |
23
|
math
|
comp_parametric_intersection_train_0332
|
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 2 letters from the multiset {j: 1, a: 1, p: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0333
|
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 {g: 4, t: 1}, 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0334
|
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: 4, v: 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}"
}
] |
44
|
math
|
comp_parametric_intersection_train_0335
|
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 2 letters from the multiset {j: 3, p: 4}, 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}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0336
|
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 2 letters from the multiset {f: 1, o: 1, d: 2, b: 2}, 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}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0337
|
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 2 letters from the multiset {z: 2, e: 1, c: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0338
|
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, s: 1, b: 1, u: 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_0339
|
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 2 letters from the multiset {o: 1, w: 1, k: 2}, 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0340
|
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: 1, h: 2, 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0341
|
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, l: 1, s: 2, q: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0342
|
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 2 letters from the multiset {j: 2, h: 4}, 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_0343
|
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 2 letters from the multiset {e: 1, w: 1, t: 1, o: 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}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0344
|
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: 1, z: 1, y: 2, v: 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}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0345
|
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 2 letters from the multiset {l: 1, p: 1, d: 2, n: 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_0346
|
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 {p: 3, z: 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}"
}
] |
51
|
math
|
comp_parametric_intersection_train_0347
|
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 2 letters from the multiset {i: 1, c: 1, q: 1, e: 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}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0348
|
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, x: 3, b: 1}, 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}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0349
|
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 2 letters from the multiset {d: 1, i: 2, z: 1, t: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0350
|
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: 1, 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}"
}
] |
27
|
math
|
comp_parametric_intersection_train_0351
|
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: 1, w: 1, x: 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}"
}
] |
4
|
math
|
comp_parametric_intersection_train_0352
|
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 2 letters from the multiset {g: 2, m: 2, t: 1, v: 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_0353
|
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 {p: 2, e: 2, a: 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}"
}
] |
51
|
math
|
comp_parametric_intersection_train_0354
|
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: 2, q: 1, w: 3, 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}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0355
|
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 2 letters from the multiset {e: 1, d: 1, b: 1, y: 1}, 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0356
|
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 2 letters from the multiset {b: 2, n: 1, r: 2, y: 1}, 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_0357
|
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 2 letters from the multiset {h: 2, a: 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}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0358
|
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: 1, l: 2, w: 1, j: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0359
|
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 2 letters from the multiset {c: 1, y: 1, w: 2, f: 1}, 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_0360
|
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, y: 1, c: 3}, 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0361
|
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: 1, v: 2, e: 4}, 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_0362
|
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 2 letters from the multiset {v: 1, s: 1, n: 1, f: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0363
|
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: 1, s: 1, o: 1, d: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0364
|
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, q: 2, l: 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}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0365
|
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: 1, l: 2, f: 1, 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0366
|
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 2 letters from the multiset {h: 2, o: 2, z: 1, t: 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_0367
|
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, k: 2, u: 1, t: 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0368
|
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 2 letters from the multiset {e: 4, n: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0369
|
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 {g: 3, x: 1, m: 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}"
}
] |
51
|
math
|
comp_parametric_intersection_train_0370
|
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: 3, n: 2}, 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0371
|
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: 4, i: 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}"
}
] |
51
|
math
|
comp_parametric_intersection_train_0372
|
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, p: 1, v: 2, i: 1}, 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0373
|
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 2 letters from the multiset {j: 1, r: 2, m: 1, f: 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}"
}
] |
12
|
math
|
comp_parametric_intersection_train_0374
|
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: 2, 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}"
}
] |
4
|
math
|
comp_parametric_intersection_train_0375
|
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 2 letters from the multiset {n: 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0376
|
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 2 letters from the multiset {w: 1, c: 3, b: 1, q: 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}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0377
|
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 2 letters from the multiset {e: 4, s: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0378
|
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, s: 5}, 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}"
}
] |
23
|
math
|
comp_parametric_intersection_train_0379
|
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 {o: 2, w: 3, u: 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}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0380
|
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 2 letters from the multiset {a: 4, o: 3}, 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}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0381
|
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 {p: 1, t: 2, e: 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0382
|
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 2 letters from the multiset {g: 1, w: 2, z: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0383
|
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: 1, y: 1, q: 2, n: 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_0384
|
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 2 letters from the multiset {u: 3, n: 3}, 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0385
|
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 2 letters from the multiset {a: 2, o: 1, w: 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}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0386
|
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 2 letters from the multiset {j: 2, d: 2, e: 2, t: 1}, 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}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0387
|
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 2 letters from the multiset {q: 3, z: 2, d: 1, g: 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_0388
|
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, v: 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}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0389
|
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 2 letters from the multiset {n: 5, d: 2}, 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0390
|
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 2 letters from the multiset {b: 2, s: 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0391
|
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 {p: 2, h: 2, n: 2, g: 1}, 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_0392
|
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 2 letters from the multiset {r: 2, q: 2, h: 1}, 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0393
|
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 2 letters from the multiset {j: 1, z: 1, g: 1, c: 1}, 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0394
|
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 {i: 2, a: 4}, 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}"
}
] |
17
|
math
|
comp_parametric_intersection_train_0395
|
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, o: 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}"
}
] |
51
|
math
|
comp_parametric_intersection_train_0396
|
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: 1, t: 1, m: 1, p: 1}, 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0397
|
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 2 letters from the multiset {n: 1, i: 1, k: 1, g: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0398
|
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 2 letters from the multiset {g: 2, o: 3}, 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0399
|
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 {i: 2, t: 1, b: 1, d: 1}, 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}"
}
] |
9
|
math
|
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