Datasets:

TTTXXX01
/

omega-combined-split-combinatory_probability_no_fixed_points

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train · 1k rows

id stringlengths 50 50	setting_key stringclasses 1 value	setting_name stringclasses 0 values	messages listlengths 1 1	ground_truth stringclasses 40 values	dataset stringclasses 1 value
combinatory_probability_no_fixed_points_train_0100	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 1, q: 1, m: 4, e: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	19	math
combinatory_probability_no_fixed_points_train_0101	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 2, r: 5}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	26	math
combinatory_probability_no_fixed_points_train_0102	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {e: 3, v: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	13	math
combinatory_probability_no_fixed_points_train_0103	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 1, e: 2, x: 1, q: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	37	math
combinatory_probability_no_fixed_points_train_0104	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 1, c: 1, n: 1, l: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	4	math
combinatory_probability_no_fixed_points_train_0105	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {i: 2, a: 1, u: 1, g: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	29	math
combinatory_probability_no_fixed_points_train_0106	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {v: 1, w: 1, i: 1, l: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	3	math
combinatory_probability_no_fixed_points_train_0107	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {c: 3, e: 1, u: 1, h: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	7	math
combinatory_probability_no_fixed_points_train_0108	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {c: 2, t: 1, k: 2, d: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	43	math
combinatory_probability_no_fixed_points_train_0109	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {u: 2, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	4	math
combinatory_probability_no_fixed_points_train_0110	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {t: 2, v: 3, p: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	29	math
combinatory_probability_no_fixed_points_train_0111	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {p: 1, f: 1, s: 2, a: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	43	math
combinatory_probability_no_fixed_points_train_0112	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 1, i: 2, h: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	7	math
combinatory_probability_no_fixed_points_train_0113	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 3, q: 1, c: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	19	math
combinatory_probability_no_fixed_points_train_0114	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 2, d: 1, l: 1, s: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	29	math
combinatory_probability_no_fixed_points_train_0115	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {z: 1, o: 2, b: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	7	math
combinatory_probability_no_fixed_points_train_0116	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 2, o: 2, l: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	17	math
combinatory_probability_no_fixed_points_train_0117	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 1, y: 2, h: 3, d: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	122	math
combinatory_probability_no_fixed_points_train_0118	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {e: 3, i: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	13	math
combinatory_probability_no_fixed_points_train_0119	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {e: 3, b: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	13	math
combinatory_probability_no_fixed_points_train_0120	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 2, o: 1, z: 3, q: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	122	math
combinatory_probability_no_fixed_points_train_0121	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 2, b: 2, u: 2, e: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	25	math
combinatory_probability_no_fixed_points_train_0122	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 3, l: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	13	math
combinatory_probability_no_fixed_points_train_0123	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 2, p: 2, w: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	7	math
combinatory_probability_no_fixed_points_train_0124	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {a: 3, n: 2, s: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	29	math
combinatory_probability_no_fixed_points_train_0125	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 1, c: 1, y: 1, d: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	4	math
combinatory_probability_no_fixed_points_train_0126	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 1, f: 1, a: 1, h: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	4	math
combinatory_probability_no_fixed_points_train_0127	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {t: 1, i: 2, x: 3, k: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	59	math
combinatory_probability_no_fixed_points_train_0128	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 1, z: 2, m: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	17	math
combinatory_probability_no_fixed_points_train_0129	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 2, a: 1, q: 1, x: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	6	math
combinatory_probability_no_fixed_points_train_0130	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 3, y: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	5	math
combinatory_probability_no_fixed_points_train_0131	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {i: 2, o: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	19	math
combinatory_probability_no_fixed_points_train_0132	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 1, v: 2, e: 2, z: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	25	math
combinatory_probability_no_fixed_points_train_0133	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 2, b: 2, q: 2, m: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	10	math
combinatory_probability_no_fixed_points_train_0134	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 4, x: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	9	math
combinatory_probability_no_fixed_points_train_0135	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {t: 1, z: 1, d: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	17	math
combinatory_probability_no_fixed_points_train_0136	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 1, f: 1, a: 3, e: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	7	math
combinatory_probability_no_fixed_points_train_0137	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 1, n: 1, f: 1, r: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	29	math
combinatory_probability_no_fixed_points_train_0138	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {x: 1, h: 3, u: 2, e: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	59	math
combinatory_probability_no_fixed_points_train_0139	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {x: 1, e: 1, w: 1, m: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	3	math
combinatory_probability_no_fixed_points_train_0140	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 1, c: 2, p: 3, q: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	122	math
combinatory_probability_no_fixed_points_train_0141	combinatory_probability_no_fixed_points	null	[ { "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, a: 2, s: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	6	math
combinatory_probability_no_fixed_points_train_0142	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {r: 3, i: 2, l: 1, n: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	59	math
combinatory_probability_no_fixed_points_train_0143	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {b: 2, n: 3, d: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	29	math
combinatory_probability_no_fixed_points_train_0144	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 1, u: 2, q: 1, g: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	29	math
combinatory_probability_no_fixed_points_train_0145	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {c: 3, x: 2, m: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	29	math
combinatory_probability_no_fixed_points_train_0146	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 3, o: 2, v: 1, l: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	122	math
combinatory_probability_no_fixed_points_train_0147	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 1, e: 1, r: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	7	math
combinatory_probability_no_fixed_points_train_0148	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {u: 1, z: 1, s: 1, m: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	3	math
combinatory_probability_no_fixed_points_train_0149	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 2, b: 1, w: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	7	math
combinatory_probability_no_fixed_points_train_0150	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 1, b: 2, l: 2, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	25	math
combinatory_probability_no_fixed_points_train_0151	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 2, n: 1, y: 1, z: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	37	math
combinatory_probability_no_fixed_points_train_0152	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 2, e: 1, s: 2, q: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	6	math
combinatory_probability_no_fixed_points_train_0153	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 1, w: 1, g: 1, q: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	4	math
combinatory_probability_no_fixed_points_train_0154	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {h: 2, x: 1, p: 2, o: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	10	math
combinatory_probability_no_fixed_points_train_0155	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 1, d: 2, s: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	17	math
combinatory_probability_no_fixed_points_train_0156	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {w: 1, x: 1, g: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	17	math
combinatory_probability_no_fixed_points_train_0157	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 2, j: 2, p: 1, n: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	6	math
combinatory_probability_no_fixed_points_train_0158	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 1, g: 3, j: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	11	math
combinatory_probability_no_fixed_points_train_0159	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 3, a: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	5	math
combinatory_probability_no_fixed_points_train_0160	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 1, b: 1, h: 2, m: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	29	math
combinatory_probability_no_fixed_points_train_0161	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 2, b: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	19	math
combinatory_probability_no_fixed_points_train_0162	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {t: 3, a: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	5	math
combinatory_probability_no_fixed_points_train_0163	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 2, r: 2, e: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	17	math
combinatory_probability_no_fixed_points_train_0164	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 1, k: 1, i: 1, x: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	4	math
combinatory_probability_no_fixed_points_train_0165	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 3, n: 2, u: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	39	math
combinatory_probability_no_fixed_points_train_0166	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 2, h: 1, g: 2, p: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	6	math
combinatory_probability_no_fixed_points_train_0167	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {e: 2, w: 2, z: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	17	math
combinatory_probability_no_fixed_points_train_0168	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {w: 1, f: 1, a: 1, p: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	3	math
combinatory_probability_no_fixed_points_train_0169	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 3, g: 2, n: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	41	math
combinatory_probability_no_fixed_points_train_0170	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {e: 4, c: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	19	math
combinatory_probability_no_fixed_points_train_0171	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 3, c: 1, a: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	38	math
combinatory_probability_no_fixed_points_train_0172	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {h: 1, v: 1, d: 1, s: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	3	math
combinatory_probability_no_fixed_points_train_0173	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {e: 4, c: 1, w: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	13	math
combinatory_probability_no_fixed_points_train_0174	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 1, c: 1, j: 1, g: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	4	math
combinatory_probability_no_fixed_points_train_0175	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {c: 1, i: 2, d: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	17	math
combinatory_probability_no_fixed_points_train_0176	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 1, t: 1, z: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	7	math
combinatory_probability_no_fixed_points_train_0177	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 1, d: 2, u: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	17	math
combinatory_probability_no_fixed_points_train_0178	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {t: 1, l: 1, d: 1, p: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	3	math
combinatory_probability_no_fixed_points_train_0179	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {o: 1, g: 1, v: 1, a: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	3	math
combinatory_probability_no_fixed_points_train_0180	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 1, j: 1, d: 2, x: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	43	math
combinatory_probability_no_fixed_points_train_0181	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 2, f: 1, w: 1, l: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	37	math
combinatory_probability_no_fixed_points_train_0182	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {v: 1, b: 1, w: 1, s: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	29	math
combinatory_probability_no_fixed_points_train_0183	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 1, p: 2, v: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	7	math
combinatory_probability_no_fixed_points_train_0184	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 1, d: 3, u: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	11	math
combinatory_probability_no_fixed_points_train_0185	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 1, m: 1, y: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	7	math
combinatory_probability_no_fixed_points_train_0186	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 2, p: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	4	math
combinatory_probability_no_fixed_points_train_0187	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 1, r: 2, u: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	17	math
combinatory_probability_no_fixed_points_train_0188	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 4, e: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	19	math
combinatory_probability_no_fixed_points_train_0189	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 2, f: 2, h: 1, w: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	6	math
combinatory_probability_no_fixed_points_train_0190	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {t: 2, b: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	4	math
combinatory_probability_no_fixed_points_train_0191	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 1, p: 1, z: 1, b: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	29	math
combinatory_probability_no_fixed_points_train_0192	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 1, w: 1, f: 2, s: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	29	math
combinatory_probability_no_fixed_points_train_0193	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {x: 2, h: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	13	math
combinatory_probability_no_fixed_points_train_0194	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {x: 3, s: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	13	math
combinatory_probability_no_fixed_points_train_0195	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 1, a: 2, u: 1, t: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	43	math
combinatory_probability_no_fixed_points_train_0196	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 1, h: 3, y: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	11	math
combinatory_probability_no_fixed_points_train_0197	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 1, m: 3, c: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as t...	11	math
combinatory_probability_no_fixed_points_train_0198	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 3, i: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the for...	5	math
combinatory_probability_no_fixed_points_train_0199	combinatory_probability_no_fixed_points	null	[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 2, o: 1, y: 3, l: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be writte...	122	math

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