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_0200	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, n: 1, l: 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...	4	math
combinatory_probability_no_fixed_points_train_0201	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 {u: 4, m: 2, t: 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...	113	math
combinatory_probability_no_fixed_points_train_0202	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: 3, d: 1, r: 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_0203	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, s: 2, q: 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_0204	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, k: 1, c: 2, o: 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_0205	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: 2, g: 1, o: 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...	41	math
combinatory_probability_no_fixed_points_train_0206	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: 4, r: 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 written as t...	13	math
combinatory_probability_no_fixed_points_train_0207	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: 2, x: 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 written as t...	17	math
combinatory_probability_no_fixed_points_train_0208	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, s: 1, e: 1, f: 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_0209	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, p: 2, v: 2, o: 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_0210	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, 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...	4	math
combinatory_probability_no_fixed_points_train_0211	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, y: 1, 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...	7	math
combinatory_probability_no_fixed_points_train_0212	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: 4, m: 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_0213	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, n: 2, q: 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_0214	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: 4, n: 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_0215	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 {f: 2, u: 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...	17	math
combinatory_probability_no_fixed_points_train_0216	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, i: 1, 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...	17	math
combinatory_probability_no_fixed_points_train_0217	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: 2, e: 1, c: 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_0218	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: 1, y: 1, p: 1, 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 writte...	3	math
combinatory_probability_no_fixed_points_train_0219	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, x: 2, t: 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...	37	math
combinatory_probability_no_fixed_points_train_0220	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, g: 1, w: 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...	43	math
combinatory_probability_no_fixed_points_train_0221	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, h: 2, f: 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...	29	math
combinatory_probability_no_fixed_points_train_0222	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: 1, u: 1, g: 1, j: 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_0223	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, r: 1, z: 1, 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...	3	math
combinatory_probability_no_fixed_points_train_0224	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: 3, f: 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_0225	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, u: 2, z: 1, 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...	25	math
combinatory_probability_no_fixed_points_train_0226	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: 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_0227	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, v: 3, n: 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...	59	math
combinatory_probability_no_fixed_points_train_0228	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, f: 1, r: 1, v: 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 writte...	7	math
combinatory_probability_no_fixed_points_train_0229	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: 3, 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 the for...	5	math
combinatory_probability_no_fixed_points_train_0230	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: 2, r: 2, 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 written as t...	7	math
combinatory_probability_no_fixed_points_train_0231	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: 2, y: 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 written as t...	17	math
combinatory_probability_no_fixed_points_train_0232	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: 4, 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...	19	math
combinatory_probability_no_fixed_points_train_0233	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, o: 1, m: 1, 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...	29	math
combinatory_probability_no_fixed_points_train_0234	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, e: 2, 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 written as t...	7	math
combinatory_probability_no_fixed_points_train_0235	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: 3, 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 written as the for...	5	math
combinatory_probability_no_fixed_points_train_0236	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, m: 1, s: 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 writte...	37	math
combinatory_probability_no_fixed_points_train_0237	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: 3, n: 3, 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 written as t...	19	math
combinatory_probability_no_fixed_points_train_0238	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, e: 3, l: 1, f: 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...	59	math
combinatory_probability_no_fixed_points_train_0239	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, b: 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_0240	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: 3, q: 1, d: 1, 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 writte...	122	math
combinatory_probability_no_fixed_points_train_0241	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, c: 3, 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 t...	11	math
combinatory_probability_no_fixed_points_train_0242	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, i: 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_0243	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, x: 1, g: 2, z: 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 writte...	122	math
combinatory_probability_no_fixed_points_train_0244	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, k: 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_0245	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, 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...	4	math
combinatory_probability_no_fixed_points_train_0246	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, o: 2, s: 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...	11	math
combinatory_probability_no_fixed_points_train_0247	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, v: 1, j: 1, o: 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_0248	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: 5, 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 written as the for...	7	math
combinatory_probability_no_fixed_points_train_0249	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: 3, n: 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_0250	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 {j: 2, v: 1, n: 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_0251	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: 3, r: 2, 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...	41	math
combinatory_probability_no_fixed_points_train_0252	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: 2, u: 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_0253	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: 2, l: 1, c: 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 writte...	10	math
combinatory_probability_no_fixed_points_train_0254	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, k: 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_0255	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, 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 the for...	5	math
combinatory_probability_no_fixed_points_train_0256	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: 3, u: 1, 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...	11	math
combinatory_probability_no_fixed_points_train_0257	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: 3, t: 1, q: 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...	7	math
combinatory_probability_no_fixed_points_train_0258	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, v: 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...	6	math
combinatory_probability_no_fixed_points_train_0259	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: 1, u: 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_0260	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: 2, o: 3, 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_0261	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, i: 1, q: 1, c: 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_0262	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: 1, i: 1, h: 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 writte...	59	math
combinatory_probability_no_fixed_points_train_0263	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: 3, z: 3, 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...	38	math
combinatory_probability_no_fixed_points_train_0264	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: 2, q: 1, r: 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...	41	math
combinatory_probability_no_fixed_points_train_0265	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: 6, b: 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...	8	math
combinatory_probability_no_fixed_points_train_0266	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: 2, t: 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_0267	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, z: 1, 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 writte...	29	math
combinatory_probability_no_fixed_points_train_0268	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: 2, r: 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 written as t...	7	math
combinatory_probability_no_fixed_points_train_0269	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 {u: 3, j: 1, p: 1, k: 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...	122	math
combinatory_probability_no_fixed_points_train_0270	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: 3, x: 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...	9	math
combinatory_probability_no_fixed_points_train_0271	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, i: 2, o: 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...	37	math
combinatory_probability_no_fixed_points_train_0272	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, s: 2, j: 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
combinatory_probability_no_fixed_points_train_0273	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, y: 1, 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...	4	math
combinatory_probability_no_fixed_points_train_0274	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, u: 1, e: 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_0275	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 {u: 3, b: 1, e: 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...	122	math
combinatory_probability_no_fixed_points_train_0276	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: 3, f: 1, 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...	11	math
combinatory_probability_no_fixed_points_train_0277	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: 2, r: 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 t...	29	math
combinatory_probability_no_fixed_points_train_0278	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, s: 3, r: 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_0279	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, d: 1, e: 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_0280	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: 3, q: 2, j: 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_0281	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: 4, 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 the for...	19	math
combinatory_probability_no_fixed_points_train_0282	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, m: 2, u: 1, b: 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 writte...	59	math
combinatory_probability_no_fixed_points_train_0283	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: 2, t: 1, e: 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...	11	math
combinatory_probability_no_fixed_points_train_0284	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: 1, r: 1, l: 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 writte...	37	math
combinatory_probability_no_fixed_points_train_0285	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, w: 1, x: 1, 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 writte...	29	math
combinatory_probability_no_fixed_points_train_0286	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, f: 2, h: 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...	25	math
combinatory_probability_no_fixed_points_train_0287	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: 1, 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 t...	11	math
combinatory_probability_no_fixed_points_train_0288	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: 2, m: 1, f: 2, j: 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_0289	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 {d: 1, t: 1, x: 3, v: 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_0290	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, a: 1, y: 1, k: 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 writte...	122	math
combinatory_probability_no_fixed_points_train_0291	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: 1, a: 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 t...	41	math
combinatory_probability_no_fixed_points_train_0292	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, 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 written as the for...	4	math
combinatory_probability_no_fixed_points_train_0293	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, k: 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...	17	math
combinatory_probability_no_fixed_points_train_0294	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, n: 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_0295	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, t: 1, j: 1, o: 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 writte...	59	math
combinatory_probability_no_fixed_points_train_0296	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, f: 1, j: 1, 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...	29	math
combinatory_probability_no_fixed_points_train_0297	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: 4, k: 2, 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...	113	math
combinatory_probability_no_fixed_points_train_0298	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, j: 3, i: 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...	122	math
combinatory_probability_no_fixed_points_train_0299	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: 3, 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 the for...	13	math

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