messages listlengths 1 1 | ground_truth stringclasses 70 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {c: 3, b: 3, e: 3}, 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... | 31 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {u: 6, z: 2}, 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 $\\frac{m}{n}$,... | 19 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 2, j: 2, q: 3, a: 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 $\\... | 59 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 1, o: 1, d: 4, u: 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 $\\... | 8 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {d: 3, j: 4}, 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 $\\frac{m}{n}$,... | 51 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {u: 3, o: 2, c: 4}, 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... | 85 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {u: 1, n: 3, s: 1, o: 1}, 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 $\\... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 3, l: 3, p: 2, n: 1}, 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 $\\... | 41 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 1, h: 1, n: 2, d: 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 $\\... | 16 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 3, j: 3}, shuffle the letters in the word, what is the probability of at least 1 letter 'a' 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 4 letters from the multiset {q: 3, p: 1, w: 3}, shuffle the letters in the word, what is the probability of at least 3 letter 'q' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 36 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 4, h: 4}, shuffle the letters in the word, what is the probability of at least 2 letter 'h' 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 3 letters from the multiset {j: 1, z: 5}, shuffle the letters in the word, what is the probability of at least 1 letter 'j' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 3, k: 3, i: 1}, 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... | 8 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 3, b: 6}, shuffle the letters in the word, what is the probability of at least 1 letter 'c' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 59 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {a: 3, n: 2, m: 1}, shuffle the letters in the word, what is the probability of at least 1 letter 'n' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 22 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 4, q: 3}, 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 $\\frac{m}{n}$,... | 54 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 1, h: 4, o: 1, y: 1}, 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 $\\... | 8 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 3, o: 3}, 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 $\\frac{m}{n}$,... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 4, i: 3}, 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 $\\frac{m}{n}$,... | 64 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 2, x: 2, 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 $\\frac{m... | 16 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 1, c: 3, o: 1, z: 1}, 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 $\\... | 6 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 1, d: 4, b: 1, u: 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 $\\... | 8 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 2, y: 2, s: 4}, 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 $\\frac{m... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 1, r: 7}, 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 $\\frac{m}{n}$,... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 3, z: 3, x: 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 $\\frac{m... | 41 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 5, d: 4}, shuffle the letters in the word, what is the probability of at least 3 letter 'm' 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 3 letters from the multiset {h: 2, w: 3, d: 4}, shuffle the letters in the word, what is the probability of at least 2 letter 'w' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 13 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {u: 2, x: 2, p: 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 $\\frac{m... | 16 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 2, z: 2, p: 2, s: 2}, 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 4 letters from the multiset {w: 3, k: 2, y: 3}, 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... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 1, f: 1, n: 1, g: 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 $\\... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 3, u: 3}, shuffle the letters in the word, what is the probability of at least 2 letter 'u' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 6 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 1, m: 4, k: 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 $\\frac{m... | 8 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {a: 3, w: 3, c: 1, s: 1}, 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 $\\... | 57 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 3, p: 1, e: 1, d: 2}, shuffle the letters in the word, what is the probability of at least 1 letter 'd' 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 3 letters from the multiset {c: 5, k: 3}, 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 $\\frac{m}{n}$,... | 19 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 2, p: 3, g: 1, h: 1}, 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 $\\... | 8 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 3, t: 2, e: 2, q: 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 $\\... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 1, x: 2, z: 3, s: 2}, 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 $\\... | 41 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {t: 4, b: 2}, shuffle the letters in the word, what is the probability of at least 1 letter 't' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 2, y: 3, w: 1}, 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 $\\frac{m... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 1, o: 1, u: 3, p: 1}, 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 $\\... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 3, g: 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 $\\frac{m}{n}$,... | 57 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 1, b: 4, n: 3}, shuffle the letters in the word, what is the probability of at least 1 letter 'j' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 5, i: 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 $\\frac{m}{n}$,... | 12 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 5, z: 4}, shuffle the letters in the word, what is the probability of at least 2 letter 'y' 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 4 letters from the multiset {m: 2, g: 3, w: 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... | 8 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 3, t: 2, m: 2, h: 2}, shuffle the letters in the word, what is the probability of at least 2 letter 't' 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 4 letters from the multiset {a: 4, e: 3, z: 2}, shuffle the letters in the word, what is the probability of at least 1 letter 'a' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 2, p: 1, y: 1, q: 2}, 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 $\\... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 4, v: 1, w: 1}, 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... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 2, g: 1, t: 4, h: 2}, shuffle the letters in the word, what is the probability of at least 2 letter 'h' 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 4 letters from the multiset {n: 5, w: 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 $\\frac{m}{n}$,... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {u: 4, x: 4}, 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 $\\frac{m}{n}$,... | 15 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 4, c: 1, z: 2, f: 1}, shuffle the letters in the word, what is the probability of at least 1 letter 't' remains in the same position?\nIf the probability can be written as the form $\\... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 2, n: 3, c: 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 $\\frac{m... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 4, x: 4}, 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 $\\frac{m}{n}$,... | 121 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 3, u: 2, g: 3}, 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... | 43 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 3, k: 2, a: 3}, 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... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 3, c: 1, t: 5}, 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... | 47 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 2, j: 2, x: 1, t: 3}, shuffle the letters in the word, what is the probability of at least 1 letter 'j' 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 4 letters from the multiset {e: 4, j: 5}, shuffle the letters in the word, what is the probability of at least 1 letter 'j' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 113 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 1, v: 2, z: 3, h: 2}, 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 $\\... | 8 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 2, e: 1, x: 3}, 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 $\\frac{m... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 1, o: 2, z: 1, d: 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 $\\... | 16 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 3, p: 2, n: 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 $\\frac{m... | 22 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 2, j: 6}, 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 $\\frac{m}{n}$,... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 2, l: 6}, shuffle the letters in the word, what is the probability of at least 2 letter 't' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 4, a: 4}, shuffle the letters in the word, what is the probability of at least 2 letter 'a' 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 3 letters from the multiset {t: 3, m: 4}, shuffle the letters in the word, what is the probability of at least 1 letter 't' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 54 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 5, c: 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 $\\frac{m}{n}$,... | 12 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 3, a: 3}, shuffle the letters in the word, what is the probability of at least 3 letter 'a' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 21 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 4, z: 3}, 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 $\\frac{m}{n}$,... | 51 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 2, y: 3, f: 2}, shuffle the letters in the word, what is the probability of at least 3 letter 'y' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 36 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 3, u: 3}, shuffle the letters in the word, what is the probability of at least 2 letter 's' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 13 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 3, u: 2, j: 2}, 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... | 57 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 1, a: 4, j: 2}, shuffle the letters in the word, what is the probability of at least 1 letter 'j' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 4 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 2, n: 4}, shuffle the letters in the word, what is the probability of at least 3 letter 'n' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 6 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {l: 2, b: 1, r: 1, s: 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 $\\... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 3, l: 3, u: 3}, 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... | 85 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {e: 1, s: 1, n: 3, u: 1}, 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 $\\... | 6 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 1, j: 4, o: 2}, 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... | 8 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 1, e: 3, t: 3, o: 1}, 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 $\\... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 3, n: 1, g: 3}, shuffle the letters in the word, what is the probability of at least 1 letter 'n' 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 4 letters from the multiset {c: 2, 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 $\\frac{m}{n}$,... | 19 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 2, r: 3, p: 2}, shuffle the letters in the word, what is the probability of at least 2 letter 'a' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 22 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 3, u: 1, i: 2}, 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 $\\frac{m... | 16 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 4, j: 2}, shuffle the letters in the word, what is the probability of at least 1 letter 't' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 28 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 5, n: 3}, shuffle the letters in the word, what is the probability of at least 1 letter 'n' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$,... | 41 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 1, i: 2, c: 2, d: 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 $\\... | 22 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {e: 4, m: 4}, 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 $\\frac{m}{n}$,... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, z: 2, x: 1, m: 3}, 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 4 letters from the multiset {m: 2, j: 4, 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... | 31 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 1, d: 2, i: 4, y: 1}, 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 $\\... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 1, n: 4, r: 3}, shuffle the letters in the word, what is the probability of at least 1 letter 'n' remains in the same position?\nIf the probability can be written as the form $\\frac{m... | 121 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {u: 4, k: 5}, 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 $\\frac{m}{n}$,... | 22 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 1, f: 1, j: 3, y: 2}, 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 $\\... | 8 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 2, p: 5}, 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 $\\frac{m}{n}$,... | 22 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {d: 3, c: 2, p: 2, o: 2}, shuffle the letters in the word, what is the probability of at least 1 letter 'd' remains in the same position?\nIf the probability can be written as the form $\\... | 41 | MATH |
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