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_0500 | 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, e: 4}, 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 th... | 44 | math |
comp_parametric_intersection_train_0501 | 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: 5, l: 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 th... | 23 | math |
comp_parametric_intersection_train_0502 | 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, y: 2, x: 1, f: 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 w... | 11 | math |
comp_parametric_intersection_train_0503 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 3, h: 4}, 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 th... | 44 | math |
comp_parametric_intersection_train_0504 | 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 4 letters from the multiset {j: 2, d: 3, h: 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... | 5 | math |
comp_parametric_intersection_train_0505 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 2, l: 3, f: 1, u: 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 w... | 5 | math |
comp_parametric_intersection_train_0506 | 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: 2, m: 2, s: 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... | 8 | math |
comp_parametric_intersection_train_0507 | 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 4 letters from the multiset {f: 1, q: 1, h: 1, w: 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 w... | 11 | math |
comp_parametric_intersection_train_0508 | 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 4 letters from the multiset {t: 4, 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 th... | 89 | math |
comp_parametric_intersection_train_0509 | 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 4 letters from the multiset {i: 4, x: 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... | 47 | math |
comp_parametric_intersection_train_0510 | 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: 5, t: 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 th... | 67 | math |
comp_parametric_intersection_train_0511 | 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: 4, k: 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 th... | 8 | math |
comp_parametric_intersection_train_0512 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 2, z: 4, 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... | 12 | math |
comp_parametric_intersection_train_0513 | 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 4 letters from the multiset {a: 1, g: 5}, 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 th... | 11 | math |
comp_parametric_intersection_train_0514 | 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, k: 3, e: 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... | 51 | math |
comp_parametric_intersection_train_0515 | 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 4 letters from the multiset {c: 2, a: 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 th... | 47 | math |
comp_parametric_intersection_train_0516 | 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 4 letters from the multiset {t: 2, m: 1, z: 1, e: 2}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be w... | 11 | math |
comp_parametric_intersection_train_0517 | 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 4 letters from the multiset {y: 2, k: 3, u: 2}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written... | 34 | math |
comp_parametric_intersection_train_0518 | 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: 3, a: 5}, 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 th... | 43 | math |
comp_parametric_intersection_train_0519 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 2, f: 3, q: 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... | 5 | math |
comp_parametric_intersection_train_0520 | 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: 3, d: 2, f: 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... | 5 | math |
comp_parametric_intersection_train_0521 | 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 4 letters from the multiset {q: 2, p: 3, b: 1}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?\nIf the probability can be written... | 11 | math |
comp_parametric_intersection_train_0522 | 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, n: 1, 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 w... | 5 | math |
comp_parametric_intersection_train_0523 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 3, t: 3, b: 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... | 51 | math |
comp_parametric_intersection_train_0524 | 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: 2, u: 2, p: 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... | 8 | math |
comp_parametric_intersection_train_0525 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 2, i: 3, u: 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... | 27 | math |
comp_parametric_intersection_train_0526 | 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 4 letters from the multiset {z: 2, t: 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 th... | 23 | math |
comp_parametric_intersection_train_0527 | 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 4 letters from the multiset {l: 2, x: 4}, 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 th... | 23 | math |
comp_parametric_intersection_train_0528 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 4, b: 4}, 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 th... | 19 | math |
comp_parametric_intersection_train_0529 | 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, d: 2, n: 2, f: 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 w... | 8 | math |
comp_parametric_intersection_train_0530 | 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 4 letters from the multiset {g: 3, q: 1, p: 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... | 11 | math |
comp_parametric_intersection_train_0531 | 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: 5, e: 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 th... | 67 | math |
comp_parametric_intersection_train_0532 | 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, o: 5}, 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 th... | 67 | math |
comp_parametric_intersection_train_0533 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 3, c: 2, u: 2}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written... | 5 | math |
comp_parametric_intersection_train_0534 | 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, s: 1, b: 4}, 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... | 19 | math |
comp_parametric_intersection_train_0535 | 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 4 letters from the multiset {z: 1, k: 5}, 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 th... | 11 | math |
comp_parametric_intersection_train_0536 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 3, o: 1, m: 2, t: 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 w... | 43 | math |
comp_parametric_intersection_train_0537 | 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 4 letters from the multiset {s: 4, e: 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 th... | 16 | math |
comp_parametric_intersection_train_0538 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 1, g: 1, f: 1, c: 5}, 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 w... | 15 | math |
comp_parametric_intersection_train_0539 | 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, z: 2, j: 2, v: 2}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be w... | 12 | math |
comp_parametric_intersection_train_0540 | 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, s: 3, r: 1, b: 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 w... | 5 | math |
comp_parametric_intersection_train_0541 | 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 4 letters from the multiset {e: 2, s: 3, k: 3}, 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... | 41 | math |
comp_parametric_intersection_train_0542 | 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 4 letters from the multiset {i: 3, z: 4, q: 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... | 41 | math |
comp_parametric_intersection_train_0543 | 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: 3, i: 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 th... | 43 | math |
comp_parametric_intersection_train_0544 | 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 4 letters from the multiset {j: 2, r: 3, k: 1, b: 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 w... | 48 | math |
comp_parametric_intersection_train_0545 | 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: 4, x: 1, y: 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... | 13 | math |
comp_parametric_intersection_train_0546 | 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: 6, o: 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 th... | 15 | math |
comp_parametric_intersection_train_0547 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 3, 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 th... | 44 | math |
comp_parametric_intersection_train_0548 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 4, u: 2, h: 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... | 44 | math |
comp_parametric_intersection_train_0549 | 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 {e: 3, j: 5}, 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 th... | 67 | math |
comp_parametric_intersection_train_0550 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 4, r: 2, b: 2}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written... | 12 | math |
comp_parametric_intersection_train_0551 | 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 4 letters from the multiset {q: 3, p: 2, d: 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... | 48 | math |
comp_parametric_intersection_train_0552 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 1, v: 1, p: 4, n: 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 w... | 13 | math |
comp_parametric_intersection_train_0553 | 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 4 letters from the multiset {d: 2, p: 4, e: 2}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?\nIf the probability can be written... | 89 | math |
comp_parametric_intersection_train_0554 | 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: 4, c: 2, 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... | 13 | math |
comp_parametric_intersection_train_0555 | 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 4 letters from the multiset {r: 1, s: 3, f: 2}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written... | 11 | math |
comp_parametric_intersection_train_0556 | 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, j: 1, e: 2, i: 2}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be w... | 13 | math |
comp_parametric_intersection_train_0557 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 2, i: 1, v: 1, c: 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 w... | 11 | math |
comp_parametric_intersection_train_0558 | 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 4 letters from the multiset {m: 3, k: 4}, 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 th... | 48 | math |
comp_parametric_intersection_train_0559 | 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, y: 1, b: 4, m: 1}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be w... | 15 | math |
comp_parametric_intersection_train_0560 | 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, a: 3, l: 2}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written... | 11 | math |
comp_parametric_intersection_train_0561 | 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, z: 2, d: 4}, 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... | 19 | math |
comp_parametric_intersection_train_0562 | 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 4 letters from the multiset {l: 3, t: 5}, 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 th... | 9 | math |
comp_parametric_intersection_train_0563 | 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 4 letters from the multiset {s: 1, l: 2, b: 2, f: 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 w... | 23 | math |
comp_parametric_intersection_train_0564 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 3, g: 4, m: 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... | 43 | math |
comp_parametric_intersection_train_0565 | 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: 3, i: 4}, 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 th... | 44 | math |
comp_parametric_intersection_train_0566 | 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: 3, x: 3}, shuffle the letters in the word, what is the probability of no letter 'x' occupy any of their original positions?\nIf the probability can be written as th... | 27 | math |
comp_parametric_intersection_train_0567 | 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: 3, c: 2, q: 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... | 43 | math |
comp_parametric_intersection_train_0568 | 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, g: 6}, 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 th... | 12 | math |
comp_parametric_intersection_train_0569 | 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 4 letters from the multiset {j: 5, a: 2}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as th... | 22 | math |
comp_parametric_intersection_train_0570 | 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: 3, q: 2, 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... | 11 | math |
comp_parametric_intersection_train_0571 | 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, q: 2, k: 3, t: 2}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be w... | 15 | math |
comp_parametric_intersection_train_0572 | 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: 4, s: 1, n: 3}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written... | 19 | math |
comp_parametric_intersection_train_0573 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 1, a: 1, r: 2, o: 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 w... | 11 | math |
comp_parametric_intersection_train_0574 | 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, b: 5}, 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 th... | 67 | math |
comp_parametric_intersection_train_0575 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 2, h: 1, i: 4}, 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... | 5 | math |
comp_parametric_intersection_train_0576 | 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 {e: 3, o: 1, d: 2, y: 2}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be w... | 15 | math |
comp_parametric_intersection_train_0577 | 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 4 letters from the multiset {s: 4, 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 th... | 23 | math |
comp_parametric_intersection_train_0578 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 2, s: 6}, 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 th... | 12 | math |
comp_parametric_intersection_train_0579 | 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 4 letters from the multiset {a: 3, d: 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 th... | 5 | math |
comp_parametric_intersection_train_0580 | 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 4 letters from the multiset {y: 4, m: 4}, 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 th... | 89 | math |
comp_parametric_intersection_train_0581 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 1, r: 2, t: 1, o: 2}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be w... | 11 | math |
comp_parametric_intersection_train_0582 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 3, q: 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 th... | 44 | math |
comp_parametric_intersection_train_0583 | 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: 4, 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 th... | 8 | math |
comp_parametric_intersection_train_0584 | 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 4 letters from the multiset {o: 2, i: 2, z: 2}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written... | 23 | math |
comp_parametric_intersection_train_0585 | 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 4 letters from the multiset {v: 4, i: 2, w: 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... | 41 | math |
comp_parametric_intersection_train_0586 | 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 4 letters from the multiset {v: 2, s: 4, d: 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... | 47 | math |
comp_parametric_intersection_train_0587 | 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 4 letters from the multiset {p: 2, o: 5}, 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 th... | 34 | math |
comp_parametric_intersection_train_0588 | 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 4 letters from the multiset {c: 2, t: 2, u: 4}, 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... | 47 | math |
comp_parametric_intersection_train_0589 | 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 4 letters from the multiset {n: 3, b: 2, p: 1, e: 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 w... | 13 | math |
comp_parametric_intersection_train_0590 | 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 4 letters from the multiset {y: 3, e: 2, m: 3}, 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... | 47 | math |
comp_parametric_intersection_train_0591 | 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 4 letters from the multiset {s: 3, d: 3, o: 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... | 48 | math |
comp_parametric_intersection_train_0592 | 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 4 letters from the multiset {g: 2, n: 1, a: 2, r: 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 w... | 13 | math |
comp_parametric_intersection_train_0593 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 1, p: 2, u: 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 w... | 51 | math |
comp_parametric_intersection_train_0594 | 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 4 letters from the multiset {m: 2, w: 2, t: 2}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written... | 23 | math |
comp_parametric_intersection_train_0595 | 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 4 letters from the multiset {z: 3, 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 th... | 5 | math |
comp_parametric_intersection_train_0596 | 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, m: 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 th... | 23 | math |
comp_parametric_intersection_train_0597 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 2, h: 2, l: 3}, 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... | 5 | math |
comp_parametric_intersection_train_0598 | 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 4 letters from the multiset {v: 4, g: 3, z: 1}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?\nIf the probability can be written... | 41 | math |
comp_parametric_intersection_train_0599 | 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: 2, k: 1, m: 2}, 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 w... | 8 | math |
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