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 {u: 3, w: 2, f: 4}, shuffle the letters in the word, what is the probability of at least 1 letter 'w' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 47 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {d: 5, g: 3}, shuffle the letters in the word, what is the probability of at least 2 letter 'g' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 33 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {k: 4, j: 5}, shuffle the letters in the word, what is the probability of at least 2 letter 'k' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 55 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {z: 2, j: 4, t: 1, r: 1}, shuffle the letters in the word, what is the probability of at least 2 letter 'z' remains in the same position?\nIf the probability can be written as the form $\\... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {s: 3, j: 6}, shuffle the letters in the word, what is the probability of at least 3 letter 's' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 85 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {y: 6, k: 3, s: 1}, shuffle the letters in the word, what is the probability of at least 1 letter 's' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {g: 2, p: 4, z: 1, k: 2}, shuffle the letters in the word, what is the probability of at least 2 letter 'p' remains in the same position?\nIf the probability can be written as the form $\\... | 55 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {b: 5, w: 4}, shuffle the letters in the word, what is the probability of at least 2 letter 'b' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 193 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {g: 5, z: 4}, shuffle the letters in the word, what is the probability of at least 2 letter 'g' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 193 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {w: 4, d: 4, x: 2}, shuffle the letters in the word, what is the probability of at least 2 letter 'd' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 26 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {n: 3, g: 5}, shuffle the letters in the word, what is the probability of at least 3 letter 'g' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 75 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {p: 5, l: 4}, shuffle the letters in the word, what is the probability of at least 1 letter 'p' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 118 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {q: 4, f: 4}, shuffle the letters in the word, what is the probability of at least 1 letter 'q' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 127 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {f: 2, v: 2, q: 2, o: 2}, shuffle the letters in the word, what is the probability of at least 1 letter 'q' remains in the same position?\nIf the probability can be written as the form $\\... | 19 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {m: 4, v: 3, r: 3}, shuffle the letters in the word, what is the probability of at least 1 letter 'v' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 35 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {s: 4, f: 2, c: 3}, shuffle the letters in the word, what is the probability of at least 3 letter 's' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 15 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {y: 4, l: 1, j: 4}, shuffle the letters in the word, what is the probability of at least 1 letter 'l' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {j: 2, y: 4, v: 1, z: 1}, shuffle the letters in the word, what is the probability of at least 2 letter 'j' remains in the same position?\nIf the probability can be written as the form $\\... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {g: 2, y: 5, p: 1}, shuffle the letters in the word, what is the probability of at least 1 letter 'g' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 19 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {a: 1, f: 2, k: 2, i: 3}, shuffle the letters in the word, what is the probability of at least 3 letter 'i' remains in the same position?\nIf the probability can be written as the form $\\... | 57 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {w: 5, t: 3}, shuffle the letters in the word, what is the probability of at least 3 letter 't' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 57 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {b: 2, f: 3, o: 3, n: 2}, shuffle the letters in the word, what is the probability of at least 2 letter 'o' remains in the same position?\nIf the probability can be written as the form $\\... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {i: 2, b: 4, o: 2, l: 2}, shuffle the letters in the word, what is the probability of at least 2 letter 'o' remains in the same position?\nIf the probability can be written as the form $\\... | 46 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {l: 4, j: 4}, shuffle the letters in the word, what is the probability of at least 1 letter 'l' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 127 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {i: 4, r: 6}, shuffle the letters in the word, what is the probability of at least 1 letter 'i' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {t: 5, n: 4}, shuffle the letters in the word, what is the probability of at least 3 letter 't' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 17 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {t: 2, b: 2, f: 1, w: 3}, shuffle the letters in the word, what is the probability of at least 1 letter 'f' remains in the same position?\nIf the probability can be written as the form $\\... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {y: 2, b: 5, n: 1, k: 2}, shuffle the letters in the word, what is the probability of at least 1 letter 'y' remains in the same position?\nIf the probability can be written as the form $\\... | 19 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {h: 2, z: 1, m: 3, c: 3}, shuffle the letters in the word, what is the probability of at least 1 letter 'z' remains in the same position?\nIf the probability can be written as the form $\\... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {s: 3, g: 2, t: 1, p: 4}, shuffle the letters in the word, what is the probability of at least 3 letter 's' remains in the same position?\nIf the probability can be written as the form $\\... | 121 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {i: 5, o: 4}, shuffle the letters in the word, what is the probability of at least 1 letter 'o' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 31 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {e: 1, w: 5, h: 1, i: 2}, shuffle the letters in the word, what is the probability of at least 1 letter 'e' remains in the same position?\nIf the probability can be written as the form $\\... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {e: 2, q: 1, l: 3, t: 2}, shuffle the letters in the word, what is the probability of at least 3 letter 'l' remains in the same position?\nIf the probability can be written as the form $\\... | 57 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {a: 3, n: 2, b: 3}, shuffle the letters in the word, what is the probability of at least 2 letter 'n' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {o: 2, r: 3, s: 3, c: 2}, shuffle the letters in the word, what is the probability of at least 2 letter 'c' remains in the same position?\nIf the probability can be written as the form $\\... | 46 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {u: 4, w: 4}, shuffle the letters in the word, what is the probability of at least 3 letter 'w' 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 {p: 2, r: 1, x: 5}, shuffle the letters in the word, what is the probability of at least 1 letter 'x' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 109 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {l: 3, x: 2, p: 3}, shuffle the letters in the word, what is the probability of at least 1 letter 'p' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 45 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {a: 1, b: 4, v: 2, m: 2}, shuffle the letters in the word, what is the probability of at least 1 letter 'b' remains in the same position?\nIf the probability can be written as the form $\\... | 31 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {b: 1, w: 4, h: 4}, shuffle the letters in the word, what is the probability of at least 1 letter 'b' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {e: 6, d: 4}, shuffle the letters in the word, what is the probability of at least 3 letter 'd' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 22 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {y: 3, u: 6}, shuffle the letters in the word, what is the probability of at least 3 letter 'u' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 61 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {r: 3, a: 6}, shuffle the letters in the word, what is the probability of at least 3 letter 'r' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 85 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {g: 4, n: 5}, shuffle the letters in the word, what is the probability of at least 3 letter 'g' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 15 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {g: 5, e: 1, b: 4}, shuffle the letters in the word, what is the probability of at least 3 letter 'g' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 8 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {c: 1, i: 2, x: 2, f: 4}, shuffle the letters in the word, what is the probability of at least 2 letter 'i' remains in the same position?\nIf the probability can be written as the form $\\... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {z: 5, d: 3}, shuffle the letters in the word, what is the probability of at least 2 letter 'd' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 33 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {p: 3, w: 1, b: 1, e: 3}, shuffle the letters in the word, what is the probability of at least 1 letter 'w' remains in the same position?\nIf the probability can be written as the form $\\... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {g: 3, u: 2, m: 2, t: 1}, shuffle the letters in the word, what is the probability of at least 1 letter 'u' remains in the same position?\nIf the probability can be written as the form $\\... | 19 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {j: 3, m: 3, h: 2}, shuffle the letters in the word, what is the probability of at least 2 letter 'm' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 33 | MATH |
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