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combinatory_pattern_matching_train_0500
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 3, k: 1, x: 1, d: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.86
math
combinatory_pattern_matching_train_0501
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, p: 3, w: 1, o: 1, x: 1}. What is the expected number of occurrences of the pattern 'n+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.14
math
combinatory_pattern_matching_train_0502
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {q: 2, r: 1, g: 1, u: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'nu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.14
math
combinatory_pattern_matching_train_0503
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 4, y: 2}, what is the expected number of times the pattern 'o*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.67
math
combinatory_pattern_matching_train_0504
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {k: 6, m: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.55
math
combinatory_pattern_matching_train_0505
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, g: 1, v: 1, q: 1, k: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0506
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {m: 2, e: 2, q: 4}. What is the expected number of occurrences of the pattern 'eq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.6
math
combinatory_pattern_matching_train_0507
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, c: 4, a: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.2
math
combinatory_pattern_matching_train_0508
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {j: 1, l: 1, q: 2, b: 1, z: 3} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0509
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 3, a: 2, m: 1, e: 1}, what is the expected number of times the pattern 'a.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.29
math
combinatory_pattern_matching_train_0510
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {a: 1, j: 2, m: 1, z: 3} to form a word, what is the expected number of matches of the pattern 'j*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.2
math
combinatory_pattern_matching_train_0511
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {k: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'k+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.33
math
combinatory_pattern_matching_train_0512
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 2, x: 2, z: 2, g: 2}, what is the expected number of times the pattern 'z+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.24
math
combinatory_pattern_matching_train_0513
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {u: 4, n: 3} to form a word, what is the expected number of matches of the pattern 'u+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.29
math
combinatory_pattern_matching_train_0514
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, y: 1, l: 3, m: 1, i: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.32
math
combinatory_pattern_matching_train_0515
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, d: 2, m: 1, y: 2, h: 1}, what is the expected number of times the pattern 'n*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.95
math
combinatory_pattern_matching_train_0516
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, m: 1, n: 1, i: 2, p: 2}, what is the expected number of times the pattern 'np*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.62
math
combinatory_pattern_matching_train_0517
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, m: 1, j: 4}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.86
math
combinatory_pattern_matching_train_0518
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {o: 1, f: 3, d: 3, l: 1} to form a word, what is the expected number of matches of the pattern 'o+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.16
math
combinatory_pattern_matching_train_0519
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {m: 1, n: 2, o: 1, g: 1, h: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0520
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {h: 1, q: 2, v: 1, d: 2, z: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.21
math
combinatory_pattern_matching_train_0521
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, w: 1, l: 2, b: 2}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0522
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 4, m: 3, t: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.64
math
combinatory_pattern_matching_train_0523
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {t: 4, l: 3}. What is the expected number of occurrences of the pattern 'l.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.71
math
combinatory_pattern_matching_train_0524
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {w: 4, e: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'w+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.86
math
combinatory_pattern_matching_train_0525
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {n: 1, o: 2, y: 1, v: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'o*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.53
math
combinatory_pattern_matching_train_0526
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {u: 5, q: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.43
math
combinatory_pattern_matching_train_0527
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, j: 1, f: 1, a: 2, v: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0528
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {u: 4, n: 3}. What is the expected number of occurrences of the pattern 'u.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.71
math
combinatory_pattern_matching_train_0529
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, x: 1, w: 1, q: 1, l: 1}. What is the expected number of occurrences of the pattern 'x.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0530
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {b: 2, x: 5, o: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.14
math
combinatory_pattern_matching_train_0531
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {n: 3, m: 4} to form a word, what is the expected number of matches of the pattern 'n*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.4
math
combinatory_pattern_matching_train_0532
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {u: 1, b: 1, i: 1, z: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'z*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.77
math
combinatory_pattern_matching_train_0533
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, s: 6}, what is the expected number of times the pattern 'u+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.46
math
combinatory_pattern_matching_train_0534
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {o: 1, u: 1, c: 1, v: 2, s: 1}. What is the expected number of occurrences of the pattern 'c.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.4
math
combinatory_pattern_matching_train_0535
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {g: 1, j: 2, n: 1, x: 1, a: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0536
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {x: 4, y: 3} to form a word, what is the expected number of matches of the pattern 'y+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.69
math
combinatory_pattern_matching_train_0537
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, g: 3}, what is the expected number of times the pattern 'x+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.74
math
combinatory_pattern_matching_train_0538
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {l: 5, k: 2}. What is the expected number of occurrences of the pattern 'l*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.38
math
combinatory_pattern_matching_train_0539
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {e: 1, n: 1, c: 1, h: 2, w: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0540
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {o: 5, p: 2}. What is the expected number of occurrences of the pattern 'po+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.67
math
combinatory_pattern_matching_train_0541
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {o: 3, c: 3, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.21
math
combinatory_pattern_matching_train_0542
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, q: 1, v: 2, e: 3}. What is the expected number of occurrences of the pattern 'yv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0543
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, r: 2, p: 2}, what is the expected number of times the pattern 'p+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.3
math
combinatory_pattern_matching_train_0544
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, y: 1, f: 5}. What is the expected number of occurrences of the pattern 'fc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.26
math
combinatory_pattern_matching_train_0545
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {c: 3, e: 4, x: 1} to form a word, what is the expected number of matches of the pattern 'x+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.16
math
combinatory_pattern_matching_train_0546
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, y: 2, t: 3}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.14
math
combinatory_pattern_matching_train_0547
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 2, p: 1, e: 3}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.2
math
combinatory_pattern_matching_train_0548
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {x: 3, g: 4}. What is the expected number of occurrences of the pattern 'g+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.29
math
combinatory_pattern_matching_train_0549
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 3, p: 4}, what is the expected number of times the pattern 'p.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.71
math
combinatory_pattern_matching_train_0550
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, f: 3, c: 1, j: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0551
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, i: 2, a: 1, w: 3}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0552
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 4, l: 1, u: 1}, what is the expected number of times the pattern 'ug+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.37
math
combinatory_pattern_matching_train_0553
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, n: 4, l: 1}. What is the expected number of occurrences of the pattern 'll+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0554
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 5, e: 3}, what is the expected number of times the pattern 'ey+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.71
math
combinatory_pattern_matching_train_0555
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, o: 1, z: 3, n: 3}, what is the expected number of times the pattern 'o*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.41
math
combinatory_pattern_matching_train_0556
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, e: 3}, what is the expected number of times the pattern 'te+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.75
math
combinatory_pattern_matching_train_0557
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {s: 2, p: 2, j: 3}. What is the expected number of occurrences of the pattern 's+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.32
math
combinatory_pattern_matching_train_0558
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, x: 1, j: 1, p: 1, k: 2}. What is the expected number of occurrences of the pattern 'x+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0559
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {t: 1, r: 1, v: 1, h: 2, x: 1}. What is the expected number of occurrences of the pattern 'rx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0560
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {d: 3, x: 3, y: 2}. What is the expected number of occurrences of the pattern 'x+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.6
math
combinatory_pattern_matching_train_0561
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, t: 4}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.2
math
combinatory_pattern_matching_train_0562
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {h: 2, q: 3, k: 1}. What is the expected number of occurrences of the pattern 'k.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.6
math
combinatory_pattern_matching_train_0563
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, y: 5}, what is the expected number of times the pattern 'y+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.71
math
combinatory_pattern_matching_train_0564
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, u: 1, s: 2, l: 2, h: 2}. What is the expected number of occurrences of the pattern 'hl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.15
math
combinatory_pattern_matching_train_0565
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 3, j: 1, v: 2, c: 2}, what is the expected number of times the pattern 'cv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.24
math
combinatory_pattern_matching_train_0566
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, m: 2, v: 1, e: 2, g: 2}. What is the expected number of occurrences of the pattern 'vt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.41
math
combinatory_pattern_matching_train_0567
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, l: 2, i: 3, a: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.21
math
combinatory_pattern_matching_train_0568
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, h: 2, a: 1, x: 1}, what is the expected number of times the pattern 'h+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.13
math
combinatory_pattern_matching_train_0569
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {a: 2, l: 3, o: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'z*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.24
math
combinatory_pattern_matching_train_0570
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, m: 3}. What is the expected number of occurrences of the pattern 'ml+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.75
math
combinatory_pattern_matching_train_0571
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, g: 2, t: 2, n: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0572
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, i: 1, n: 5}, what is the expected number of times the pattern 'n.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.36
math
combinatory_pattern_matching_train_0573
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {v: 2, s: 3, h: 2, p: 1} to form a word, what is the expected number of matches of the pattern 's.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.32
math
combinatory_pattern_matching_train_0574
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, i: 2, z: 1, u: 2, h: 1}, what is the expected number of times the pattern 'm.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.07
math
combinatory_pattern_matching_train_0575
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, j: 2, a: 3, h: 1}, what is the expected number of times the pattern 'h+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.07
math
combinatory_pattern_matching_train_0576
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, m: 2, i: 2, n: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0577
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {m: 1, t: 1, u: 1, d: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'u.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.07
math
combinatory_pattern_matching_train_0578
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {f: 1, x: 1, i: 1, k: 1, n: 4} to form a word, what is the expected number of matches of the pattern 'x*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.41
math
combinatory_pattern_matching_train_0579
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {q: 1, w: 2, r: 1, i: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0580
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, w: 1, t: 2, m: 2, z: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0581
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 1, d: 2, o: 2, m: 1, z: 2}, what is the expected number of times the pattern 'zo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.24
math
combinatory_pattern_matching_train_0582
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, u: 1, e: 3}. What is the expected number of occurrences of the pattern 'e.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.21
math
combinatory_pattern_matching_train_0583
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, x: 2, i: 1, s: 2}, what is the expected number of times the pattern 's.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.29
math
combinatory_pattern_matching_train_0584
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {j: 1, c: 3, w: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'c+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
math
combinatory_pattern_matching_train_0585
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, j: 2, y: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.14
math
combinatory_pattern_matching_train_0586
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 4, p: 4}, what is the expected number of times the pattern 'pv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.2
math
combinatory_pattern_matching_train_0587
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 5, a: 1, g: 1}, what is the expected number of times the pattern 'af*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.19
math
combinatory_pattern_matching_train_0588
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {d: 1, u: 2, w: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'wd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0589
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, n: 4, r: 1}. What is the expected number of occurrences of the pattern 'f.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.4
math
combinatory_pattern_matching_train_0590
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {j: 1, f: 3, l: 4} to form a word, what is the expected number of matches of the pattern 'l.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.21
math
combinatory_pattern_matching_train_0591
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {n: 1, v: 3, c: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'n+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.21
math
combinatory_pattern_matching_train_0592
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, w: 2, k: 2, p: 2}, what is the expected number of times the pattern 'm+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.14
math
combinatory_pattern_matching_train_0593
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, t: 2, v: 1, b: 1, y: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0594
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, v: 2, k: 2}. What is the expected number of occurrences of the pattern 'z+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.3
math
combinatory_pattern_matching_train_0595
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 1, m: 3, v: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.86
math
combinatory_pattern_matching_train_0596
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {q: 3, i: 4, b: 1} to form a word, what is the expected number of matches of the pattern 'ib*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.64
math
combinatory_pattern_matching_train_0597
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {b: 1, z: 2, j: 1, e: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'e.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
math
combinatory_pattern_matching_train_0598
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, j: 1, d: 3, r: 2}. What is the expected number of occurrences of the pattern 'd+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.4
math
combinatory_pattern_matching_train_0599
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, x: 1, t: 1, v: 3}, what is the expected number of times the pattern 'k*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.7
math