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_0200
|
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: 4, t: 1, 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}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0201
|
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: 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}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0202
|
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: 2, b: 2, p: 1, e: 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}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0203
|
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: 3, l: 1, f: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0204
|
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, v: 1, n: 1, s: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0205
|
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, k: 1, l: 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}"
}
] |
12
|
math
|
comp_parametric_intersection_train_0206
|
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, y: 1, x: 2, v: 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_0207
|
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: 2, c: 1, z: 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0208
|
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: 3, u: 1}, 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_0209
|
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, k: 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}"
}
] |
6
|
math
|
comp_parametric_intersection_train_0210
|
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 {k: 1, t: 3, j: 1, a: 1}, 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}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0211
|
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 {t: 1, d: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0212
|
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, v: 1, d: 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_0213
|
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, q: 1, p: 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}"
}
] |
10
|
math
|
comp_parametric_intersection_train_0214
|
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: 4, w: 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}"
}
] |
17
|
math
|
comp_parametric_intersection_train_0215
|
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: 1, y: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0216
|
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: 2, 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0217
|
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: 1, c: 2, b: 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_0218
|
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, q: 1, h: 1, o: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0219
|
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: 4, l: 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}"
}
] |
44
|
math
|
comp_parametric_intersection_train_0220
|
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, b: 2, o: 1, f: 1}, 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_0221
|
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, c: 1, r: 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0222
|
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, b: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0223
|
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: 2, v: 1, z: 1, 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0224
|
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: 1, w: 1, u: 2, a: 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}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0225
|
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, b: 1, j: 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}"
}
] |
27
|
math
|
comp_parametric_intersection_train_0226
|
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: 1, y: 1, s: 1, c: 1}, 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0227
|
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: 1, w: 1, a: 1, k: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0228
|
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: 1, x: 1, f: 1, o: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0229
|
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: 2, m: 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}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0230
|
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: 3, k: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0231
|
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: 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_0232
|
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: 3, y: 2, d: 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}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0233
|
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: 1, i: 1, n: 1, g: 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_0234
|
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, f: 3, 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}"
}
] |
12
|
math
|
comp_parametric_intersection_train_0235
|
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, n: 3, 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}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0236
|
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, c: 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}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0237
|
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, t: 3, q: 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0238
|
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, r: 1, l: 1, m: 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}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0239
|
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: 4, h: 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}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0240
|
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, x: 3, y: 1, h: 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}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0241
|
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, n: 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}"
}
] |
17
|
math
|
comp_parametric_intersection_train_0242
|
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: 5, d: 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_0243
|
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, m: 3}, 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0244
|
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: 2, o: 2, d: 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_0245
|
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: 3, n: 1, x: 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}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0246
|
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, j: 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0247
|
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, h: 2, z: 2, t: 1}, 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_0248
|
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, z: 1, h: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0249
|
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, y: 1, t: 2, g: 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}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0250
|
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: 2, f: 1, z: 2, 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_0251
|
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: 3, h: 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_0252
|
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, 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}"
}
] |
4
|
math
|
comp_parametric_intersection_train_0253
|
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: 3, 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_0254
|
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: 1, e: 2, v: 2, c: 1}, 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_0255
|
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: 1, o: 4}, 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0256
|
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, e: 2, y: 1, a: 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_0257
|
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: 2, b: 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}"
}
] |
4
|
math
|
comp_parametric_intersection_train_0258
|
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, 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}"
}
] |
4
|
math
|
comp_parametric_intersection_train_0259
|
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, n: 1, s: 1, l: 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_0260
|
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, v: 1, 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}"
}
] |
4
|
math
|
comp_parametric_intersection_train_0261
|
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, l: 1, u: 1, h: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0262
|
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: 1, j: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0263
|
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, r: 1, f: 1, m: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0264
|
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, t: 1, p: 1, l: 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}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0265
|
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, p: 1, k: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0266
|
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, o: 2, m: 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_0267
|
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, n: 2, l: 2, x: 1}, 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_0268
|
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, d: 1, s: 3}, 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}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0269
|
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, o: 2, y: 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_0270
|
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, c: 1, y: 2, n: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0271
|
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, a: 2, c: 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_0272
|
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, s: 1, k: 1, g: 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_0273
|
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, x: 3}, 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_0274
|
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, k: 2, n: 1, o: 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_0275
|
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, o: 4}, 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}"
}
] |
10
|
math
|
comp_parametric_intersection_train_0276
|
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}, 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}"
}
] |
4
|
math
|
comp_parametric_intersection_train_0277
|
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, q: 2, t: 1}, 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_0278
|
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, n: 1, c: 1, s: 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}"
}
] |
11
|
math
|
comp_parametric_intersection_train_0279
|
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, m: 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}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0280
|
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, 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}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0281
|
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: 3, 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}"
}
] |
3
|
math
|
comp_parametric_intersection_train_0282
|
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: 2, u: 2, q: 1, y: 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_0283
|
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 {k: 2, f: 2, l: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0284
|
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: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0285
|
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, v: 1, y: 2, 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}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0286
|
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, o: 1, t: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0287
|
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: 1, n: 2, x: 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}"
}
] |
5
|
math
|
comp_parametric_intersection_train_0288
|
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, g: 2, m: 1}, 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0289
|
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: 1, i: 1, o: 2, b: 1}, 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_0290
|
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: 1, o: 1, w: 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}"
}
] |
13
|
math
|
comp_parametric_intersection_train_0291
|
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: 2, s: 2, 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}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0292
|
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: 1, f: 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0293
|
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, n: 2, z: 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}"
}
] |
27
|
math
|
comp_parametric_intersection_train_0294
|
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: 2, b: 1, j: 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}"
}
] |
4
|
math
|
comp_parametric_intersection_train_0295
|
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, x: 1, t: 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}"
}
] |
8
|
math
|
comp_parametric_intersection_train_0296
|
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: 1, b: 1, p: 1}, 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}"
}
] |
7
|
math
|
comp_parametric_intersection_train_0297
|
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, v: 1, q: 1, a: 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0298
|
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, t: 1, p: 2, 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}"
}
] |
9
|
math
|
comp_parametric_intersection_train_0299
|
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, d: 1, v: 2, b: 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}"
}
] |
11
|
math
|
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