messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {x: 6, e: 4}, shuffle the letters in the word, what is the probability of exact 3 letter 'x' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 26 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {d: 2, f: 1, k: 4, a: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'a' remains in the same position?\nIf the probability can be written as the form $\\fra... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {y: 2, x: 3, g: 1, w: 4}, shuffle the letters in the word, what is the probability of exact 3 letter 'w' remains in the same position?\nIf the probability can be written as the form $\\fra... | 73 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {q: 3, w: 3, h: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'w' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 47 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {t: 1, h: 4, m: 1, z: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'z' remains in the same position?\nIf the probability can be written as the form $\\fra... | 85 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {r: 5, p: 2, a: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'p' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 46 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {h: 4, r: 5}, shuffle the letters in the word, what is the probability of exact 1 letter 'h' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 89 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {p: 3, f: 3, s: 2, w: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'f' remains in the same position?\nIf the probability can be written as the form $\\fra... | 131 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {d: 4, i: 2, g: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'g' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 39 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {j: 4, e: 5}, shuffle the letters in the word, what is the probability of exact 2 letter 'e' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 83 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {z: 2, j: 6}, shuffle the letters in the word, what is the probability of exact 1 letter 'j' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 31 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {m: 1, s: 2, p: 4, x: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'p' remains in the same position?\nIf the probability can be written as the form $\\fra... | 25 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {o: 3, g: 5}, shuffle the letters in the word, what is the probability of exact 3 letter 'o' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 57 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {k: 1, q: 4, u: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'k' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {q: 3, p: 5}, shuffle the letters in the word, what is the probability of exact 2 letter 'q' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 65 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {r: 4, z: 5}, shuffle the letters in the word, what is the probability of exact 3 letter 'r' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {t: 7, j: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'j' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 163 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {g: 2, b: 6}, shuffle the letters in the word, what is the probability of exact 1 letter 'b' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 31 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {r: 4, i: 3, q: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'q' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 163 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {y: 4, g: 4, m: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'g' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 25 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {o: 5, q: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'o' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 75 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {t: 3, y: 1, l: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 't' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {i: 4, b: 2, q: 2}, shuffle the letters in the word, what is the probability of exact 3 letter 'i' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {j: 2, h: 2, t: 1, i: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'j' remains in the same position?\nIf the probability can be written as the form $\\fra... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {q: 2, y: 1, v: 2, i: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'v' remains in the same position?\nIf the probability can be written as the form $\\fra... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {y: 3, o: 3, t: 1, i: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'o' remains in the same position?\nIf the probability can be written as the form $\\fra... | 47 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {o: 2, h: 3, n: 2, p: 1}, shuffle the letters in the word, what is the probability of exact 2 letter 'o' remains in the same position?\nIf the probability can be written as the form $\\fra... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {m: 3, u: 3, s: 2, v: 2}, shuffle the letters in the word, what is the probability of exact 3 letter 'm' remains in the same position?\nIf the probability can be written as the form $\\fra... | 121 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {n: 4, w: 3, d: 2}, shuffle the letters in the word, what is the probability of exact 3 letter 'n' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {b: 3, u: 3, i: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'i' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 39 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {u: 4, r: 1, c: 2, e: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'e' remains in the same position?\nIf the probability can be written as the form $\\fra... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {r: 2, o: 4, s: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'r' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {s: 4, q: 3, o: 2}, shuffle the letters in the word, what is the probability of exact 3 letter 's' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {d: 5, l: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'd' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 71 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {b: 1, h: 1, y: 1, v: 5}, shuffle the letters in the word, what is the probability of exact 2 letter 'v' remains in the same position?\nIf the probability can be written as the form $\\fra... | 75 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {v: 2, r: 2, g: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'r' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {a: 3, w: 2, p: 1, e: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'w' remains in the same position?\nIf the probability can be written as the form $\\fra... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {i: 4, d: 2, a: 2, s: 2}, shuffle the letters in the word, what is the probability of exact 3 letter 'i' remains in the same position?\nIf the probability can be written as the form $\\fra... | 73 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {a: 6, m: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'm' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 39 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {z: 3, e: 4, h: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'z' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 121 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {i: 4, f: 1, b: 2, x: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'x' remains in the same position?\nIf the probability can be written as the form $\\fra... | 163 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {q: 6, h: 4}, shuffle the letters in the word, what is the probability of exact 3 letter 'h' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 73 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {h: 1, b: 2, z: 3, o: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'o' remains in the same position?\nIf the probability can be written as the form $\\fra... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {a: 1, x: 3, h: 5}, shuffle the letters in the word, what is the probability of exact 2 letter 'x' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 47 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {a: 7, y: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'y' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 131 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {p: 2, e: 2, l: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'e' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {j: 2, v: 6}, shuffle the letters in the word, what is the probability of exact 1 letter 'j' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {d: 1, n: 3, m: 4, z: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'z' remains in the same position?\nIf the probability can be written as the form $\\fra... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {x: 4, i: 6}, shuffle the letters in the word, what is the probability of exact 3 letter 'i' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 26 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {h: 4, s: 1, b: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'h' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 89 | MATH |
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