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_0100 | comp_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: 1, z: 1, x: 4}, 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_0101 | comp_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: 3, g: 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}"
}
] | 6 | math |
comp_parametric_intersection_train_0102 | comp_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: 4, g: 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}"
}
] | 4 | math |
comp_parametric_intersection_train_0103 | comp_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, w: 2, r: 1, v: 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_0104 | comp_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, e: 1, f: 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}"
}
] | 7 | math |
comp_parametric_intersection_train_0105 | comp_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, s: 1, t: 1, 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}"
}
] | 7 | math |
comp_parametric_intersection_train_0106 | comp_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: 2, i: 1, 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}"
}
] | 7 | math |
comp_parametric_intersection_train_0107 | comp_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, e: 1, k: 1, y: 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}"
}
] | 7 | math |
comp_parametric_intersection_train_0108 | comp_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: 5, f: 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}"
}
] | 12 | math |
comp_parametric_intersection_train_0109 | comp_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, q: 1, k: 2, 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}"
}
] | 51 | math |
comp_parametric_intersection_train_0110 | comp_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, s: 2, y: 1, z: 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}"
}
] | 3 | math |
comp_parametric_intersection_train_0111 | comp_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: 3, q: 2}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 6 | math |
comp_parametric_intersection_train_0112 | comp_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, r: 2, z: 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}"
}
] | 8 | math |
comp_parametric_intersection_train_0113 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {u: 2, i: 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}"
}
] | 3 | math |
comp_parametric_intersection_train_0114 | comp_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: 3, s: 1, n: 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}"
}
] | 11 | math |
comp_parametric_intersection_train_0115 | comp_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, n: 5}, 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_0116 | comp_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: 2, o: 2, y: 1, 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}"
}
] | 11 | math |
comp_parametric_intersection_train_0117 | comp_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: 4, 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}"
}
] | 11 | math |
comp_parametric_intersection_train_0118 | comp_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, j: 1, c: 1, p: 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}"
}
] | 9 | math |
comp_parametric_intersection_train_0119 | comp_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, p: 1, n: 1, 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}"
}
] | 51 | math |
comp_parametric_intersection_train_0120 | comp_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: 2, d: 4}, 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_0121 | comp_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: 1, j: 1, d: 1, h: 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_0122 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 5, z: 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}"
}
] | 23 | math |
comp_parametric_intersection_train_0123 | comp_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}, 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_0124 | comp_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, y: 1, q: 1, k: 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_0125 | comp_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, 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_0126 | comp_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: 1, t: 2, 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_0127 | comp_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, m: 4, z: 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}"
}
] | 13 | math |
comp_parametric_intersection_train_0128 | comp_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, m: 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}"
}
] | 7 | math |
comp_parametric_intersection_train_0129 | comp_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, y: 2, d: 1, c: 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}"
}
] | 11 | math |
comp_parametric_intersection_train_0130 | comp_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, o: 2, s: 2, 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}"
}
] | 12 | math |
comp_parametric_intersection_train_0131 | comp_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, v: 3}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 6 | math |
comp_parametric_intersection_train_0132 | comp_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: 5, 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}"
}
] | 12 | math |
comp_parametric_intersection_train_0133 | comp_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, w: 2, n: 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}"
}
] | 3 | math |
comp_parametric_intersection_train_0134 | comp_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: 4, r: 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}"
}
] | 4 | math |
comp_parametric_intersection_train_0135 | comp_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: 2, c: 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}"
}
] | 4 | math |
comp_parametric_intersection_train_0136 | comp_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: 1, i: 1, o: 2, y: 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}"
}
] | 12 | math |
comp_parametric_intersection_train_0137 | comp_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, r: 3, q: 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}"
}
] | 11 | math |
comp_parametric_intersection_train_0138 | comp_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: 2, g: 4}, 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_0139 | comp_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, c: 6}, 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}"
}
] | 8 | math |
comp_parametric_intersection_train_0140 | comp_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, e: 1, d: 2}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
comp_parametric_intersection_train_0141 | comp_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, i: 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}"
}
] | 27 | math |
comp_parametric_intersection_train_0142 | comp_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: 3, u: 1, 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_0143 | comp_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: 3, h: 1, j: 3}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 11 | math |
comp_parametric_intersection_train_0144 | comp_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, d: 1, y: 1, o: 3}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 11 | math |
comp_parametric_intersection_train_0145 | comp_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, e: 1, v: 2, a: 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}"
}
] | 9 | math |
comp_parametric_intersection_train_0146 | comp_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, h: 2, d: 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_0147 | comp_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, q: 1, a: 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_0148 | comp_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, j: 1, e: 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}"
}
] | 4 | math |
comp_parametric_intersection_train_0149 | comp_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, v: 2, z: 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}"
}
] | 8 | math |
comp_parametric_intersection_train_0150 | comp_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: 2, f: 3}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 7 | math |
comp_parametric_intersection_train_0151 | comp_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, i: 1, e: 1, f: 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}"
}
] | 9 | math |
comp_parametric_intersection_train_0152 | comp_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, e: 3, 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}"
}
] | 8 | math |
comp_parametric_intersection_train_0153 | comp_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: 2, n: 1, s: 4}, 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}"
}
] | 44 | math |
comp_parametric_intersection_train_0154 | comp_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: 3, 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}"
}
] | 8 | math |
comp_parametric_intersection_train_0155 | comp_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, v: 1, m: 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}"
}
] | 4 | math |
comp_parametric_intersection_train_0156 | comp_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: 4, e: 1, w: 1, k: 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}"
}
] | 44 | math |
comp_parametric_intersection_train_0157 | comp_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, n: 1, u: 1, e: 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}"
}
] | 11 | math |
comp_parametric_intersection_train_0158 | comp_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: 1, i: 5}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 11 | math |
comp_parametric_intersection_train_0159 | comp_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, 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}"
}
] | 3 | math |
comp_parametric_intersection_train_0160 | comp_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, q: 1, g: 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_0161 | comp_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, h: 2, u: 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}"
}
] | 11 | math |
comp_parametric_intersection_train_0162 | comp_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, p: 1, q: 2, 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}"
}
] | 51 | math |
comp_parametric_intersection_train_0163 | comp_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: 3, i: 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}"
}
] | 7 | math |
comp_parametric_intersection_train_0164 | comp_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, d: 3, q: 2}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 51 | math |
comp_parametric_intersection_train_0165 | comp_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, l: 1, q: 1, x: 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_0166 | comp_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, k: 3, c: 1, y: 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}"
}
] | 51 | math |
comp_parametric_intersection_train_0167 | comp_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, d: 3}, shuffle the letters in the word, what is the probability of no letter 'a' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 7 | math |
comp_parametric_intersection_train_0168 | comp_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: 3, 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}"
}
] | 3 | math |
comp_parametric_intersection_train_0169 | comp_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, d: 1, v: 2, o: 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}"
}
] | 12 | math |
comp_parametric_intersection_train_0170 | comp_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: 5, i: 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}"
}
] | 13 | math |
comp_parametric_intersection_train_0171 | comp_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, u: 2, x: 2, p: 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}"
}
] | 5 | math |
comp_parametric_intersection_train_0172 | comp_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, x: 2, m: 1, i: 2}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 5 | math |
comp_parametric_intersection_train_0173 | comp_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: 2, w: 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}"
}
] | 7 | math |
comp_parametric_intersection_train_0174 | comp_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, p: 3, g: 1, i: 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}"
}
] | 3 | math |
comp_parametric_intersection_train_0175 | comp_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, u: 1, r: 2, w: 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}"
}
] | 11 | math |
comp_parametric_intersection_train_0176 | comp_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: 1, c: 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_0177 | comp_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: 3, c: 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}"
}
] | 6 | math |
comp_parametric_intersection_train_0178 | comp_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, t: 3}, 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_0179 | comp_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: 3, v: 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}"
}
] | 51 | math |
comp_parametric_intersection_train_0180 | comp_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, p: 3, r: 1, b: 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}"
}
] | 3 | math |
comp_parametric_intersection_train_0181 | comp_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: 1, z: 1, h: 1, o: 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_0182 | comp_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, b: 1, u: 3}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 9 | math |
comp_parametric_intersection_train_0183 | comp_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, q: 2, f: 3}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 11 | math |
comp_parametric_intersection_train_0184 | comp_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, k: 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_0185 | comp_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: 3, a: 1, j: 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_0186 | comp_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: 2, s: 2, 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_0187 | comp_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: 3, v: 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_0188 | comp_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, w: 1, l: 1, 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}"
}
] | 7 | math |
comp_parametric_intersection_train_0189 | comp_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, m: 3}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 7 | math |
comp_parametric_intersection_train_0190 | comp_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, e: 1, k: 3, j: 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}"
}
] | 13 | math |
comp_parametric_intersection_train_0191 | comp_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, u: 1, n: 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_0192 | comp_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: 2, m: 1, d: 1}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 7 | math |
comp_parametric_intersection_train_0193 | comp_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, e: 1, m: 1, w: 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}"
}
] | 9 | math |
comp_parametric_intersection_train_0194 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 1, i: 1, g: 1, q: 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_0195 | comp_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, v: 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}"
}
] | 9 | math |
comp_parametric_intersection_train_0196 | comp_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: 4, m: 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}"
}
] | 44 | math |
comp_parametric_intersection_train_0197 | comp_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, c: 3, a: 1, l: 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}"
}
] | 13 | math |
comp_parametric_intersection_train_0198 | comp_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: 2, p: 2, s: 1, z: 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}"
}
] | 5 | math |
comp_parametric_intersection_train_0199 | comp_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, f: 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 |
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