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combinatory_pattern_matching_train_0700
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, r: 3, c: 2}, what is the expected number of times the pattern 'c+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.31
math
combinatory_pattern_matching_train_0701
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 3, k: 3, b: 2}, what is the expected number of times the pattern 'k*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.4
math
combinatory_pattern_matching_train_0702
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {n: 2, x: 1, b: 5} to form a word, what is the expected number of matches of the pattern 'n+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.6
math
combinatory_pattern_matching_train_0703
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 1, o: 1, c: 2, n: 1, f: 1}, what is the expected number of times the pattern 'dn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0704
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {w: 2, q: 2, j: 3, c: 1}. What is the expected number of occurrences of the pattern 'cq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.62
math
combinatory_pattern_matching_train_0705
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, j: 5}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.0
math
combinatory_pattern_matching_train_0706
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 3, e: 1, i: 1, u: 1, g: 1}, what is the expected number of times the pattern 'ou*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.93
math
combinatory_pattern_matching_train_0707
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {w: 1, s: 1, z: 2, o: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0708
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {n: 1, g: 1, f: 1, b: 1, y: 3} to form a word, what is the expected number of matches of the pattern 'g+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.05
math
combinatory_pattern_matching_train_0709
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {u: 2, o: 3, k: 1} to form a word, what is the expected number of matches of the pattern 'k+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.3
math
combinatory_pattern_matching_train_0710
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, r: 1, d: 1, p: 3, i: 2}, what is the expected number of times the pattern 'r+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.04
math
combinatory_pattern_matching_train_0711
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, b: 1, k: 3, f: 3}. What is the expected number of occurrences of the pattern 'gf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.5
math
combinatory_pattern_matching_train_0712
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {o: 1, i: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.86
math
combinatory_pattern_matching_train_0713
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 2, l: 1, y: 1, s: 3}, what is the expected number of times the pattern 'l*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.64
math
combinatory_pattern_matching_train_0714
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {q: 3, j: 1, w: 1, b: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'm*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.86
math
combinatory_pattern_matching_train_0715
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, u: 2}, what is the expected number of times the pattern 'c.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.8
math
combinatory_pattern_matching_train_0716
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {v: 4, l: 2} to form a word, what is the expected number of matches of the pattern 'l+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.93
math
combinatory_pattern_matching_train_0717
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {i: 4, r: 3}. What is the expected number of occurrences of the pattern 'ir+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.69
math
combinatory_pattern_matching_train_0718
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 3, o: 3, a: 2}, what is the expected number of times the pattern 'os+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.6
math
combinatory_pattern_matching_train_0719
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {o: 1, h: 1, v: 3, a: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'vo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.14
math
combinatory_pattern_matching_train_0720
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {l: 1, w: 2, y: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'f*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.53
math
combinatory_pattern_matching_train_0721
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, e: 2, y: 1, x: 2, u: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0722
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {j: 2, c: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'cj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.32
math
combinatory_pattern_matching_train_0723
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {m: 2, i: 1, l: 3, t: 1}. What is the expected number of occurrences of the pattern 'm*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.2
math
combinatory_pattern_matching_train_0724
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 1, e: 2, c: 1, n: 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}" } ]
0.4
math
combinatory_pattern_matching_train_0725
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {f: 1, v: 2, n: 1, j: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0726
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 3, e: 4}, what is the expected number of times the pattern 'e+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.29
math
combinatory_pattern_matching_train_0727
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {t: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'tu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.33
math
combinatory_pattern_matching_train_0728
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, a: 2, n: 2, b: 1}. What is the expected number of occurrences of the pattern 'o*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.53
math
combinatory_pattern_matching_train_0729
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, e: 3, k: 2}. What is the expected number of occurrences of the pattern 'u+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.31
math
combinatory_pattern_matching_train_0730
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {n: 1, c: 4, s: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'nc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.68
math
combinatory_pattern_matching_train_0731
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {p: 1, d: 2, a: 1, j: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'd+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.15
math
combinatory_pattern_matching_train_0732
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, c: 3}, 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}" } ]
0.74
math
combinatory_pattern_matching_train_0733
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, w: 2, k: 3}, 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}" } ]
0.2
math
combinatory_pattern_matching_train_0734
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {w: 1, y: 2, l: 3, o: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0735
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, t: 2, a: 1, d: 1, p: 1}. What is the expected number of occurrences of the pattern 't*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.65
math
combinatory_pattern_matching_train_0736
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {a: 1, m: 3, g: 2, c: 2}. What is the expected number of occurrences of the pattern 'a.*g' 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_0737
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, t: 3, i: 2}. What is the expected number of occurrences of the pattern 'i.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.86
math
combinatory_pattern_matching_train_0738
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {z: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'z+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.6
math
combinatory_pattern_matching_train_0739
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {h: 1, r: 1, m: 1, e: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0740
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, a: 5}, 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}" } ]
0.14
math
combinatory_pattern_matching_train_0741
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 3, j: 2, u: 3}, what is the expected number of times the pattern 'uy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.6
math
combinatory_pattern_matching_train_0742
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, e: 4, v: 2}. What is the expected number of occurrences of the pattern 'v.*m' 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_0743
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, i: 1, e: 1, v: 2, f: 2}, what is the expected number of times the pattern 'f.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.14
math
combinatory_pattern_matching_train_0744
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {t: 1, x: 2, i: 2, a: 1, d: 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}" } ]
0.11
math
combinatory_pattern_matching_train_0745
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, n: 2, v: 1, d: 2, y: 1}. What is the expected number of occurrences of the pattern 'v*d' 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_0746
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {x: 2, t: 1, q: 2, h: 2, b: 1} to form a word, what is the expected number of matches of the pattern 't.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.21
math
combinatory_pattern_matching_train_0747
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {u: 5, p: 3}. What is the expected number of occurrences of the pattern 'u*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.84
math
combinatory_pattern_matching_train_0748
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 4, d: 4}, what is the expected number of times the pattern 'd+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.5
math
combinatory_pattern_matching_train_0749
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, t: 2, h: 2}, 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}" } ]
0.47
math
combinatory_pattern_matching_train_0750
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {h: 1, v: 3, q: 1, t: 1, 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_0751
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {p: 3, f: 2, s: 3} to form a word, what is the expected number of matches of the pattern 'f*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.36
math
combinatory_pattern_matching_train_0752
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {i: 6, a: 2} to form a word, what is the expected number of matches of the pattern 'ai*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.36
math
combinatory_pattern_matching_train_0753
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {w: 1, n: 1, u: 2, m: 1, p: 1}. What is the expected number of occurrences of the pattern 'p+w' 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_0754
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {w: 4, s: 3} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.71
math
combinatory_pattern_matching_train_0755
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {f: 4, e: 2}. What is the expected number of occurrences of the pattern 'e.*e' 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_0756
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 4, z: 3}, 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}" } ]
0.86
math
combinatory_pattern_matching_train_0757
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, p: 6}. What is the expected number of occurrences of the pattern 'p*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.86
math
combinatory_pattern_matching_train_0758
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {h: 3, l: 2, f: 1, s: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'n+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.05
math
combinatory_pattern_matching_train_0759
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, h: 3, m: 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}" } ]
0.64
math
combinatory_pattern_matching_train_0760
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {b: 5, q: 1}. What is the expected number of occurrences of the pattern 'q.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.0
math
combinatory_pattern_matching_train_0761
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 4, u: 4}, what is the expected number of times the pattern 'n+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.2
math
combinatory_pattern_matching_train_0762
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 2, z: 2, h: 4}, what is the expected number of times the pattern 'z*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.24
math
combinatory_pattern_matching_train_0763
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, p: 2, h: 2}, what is the expected number of times the pattern 'eh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.8
math
combinatory_pattern_matching_train_0764
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {k: 2, y: 4, m: 2}. What is the expected number of occurrences of the pattern 'k+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.48
math
combinatory_pattern_matching_train_0765
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 3, d: 1, u: 1, s: 1}, what is the expected number of times the pattern 'u.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.6
math
combinatory_pattern_matching_train_0766
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 2, i: 2, p: 1, a: 1, x: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.29
math
combinatory_pattern_matching_train_0767
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, q: 1, j: 1, l: 2, r: 1}. What is the expected number of occurrences of the pattern 'rg+' 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_0768
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {f: 3, h: 1, u: 3} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0769
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {t: 2, r: 1, m: 2, y: 1}. What is the expected number of occurrences of the pattern 't+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.23
math
combinatory_pattern_matching_train_0770
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 1, q: 2, w: 2, t: 2}, what is the expected number of times the pattern 'w.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.57
math
combinatory_pattern_matching_train_0771
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {p: 4, s: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.4
math
combinatory_pattern_matching_train_0772
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, j: 4}, what is the expected number of times the pattern 'j*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.73
math
combinatory_pattern_matching_train_0773
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {i: 2, l: 4, c: 2} to form a word, what is the expected number of matches of the pattern 'l*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.6
math
combinatory_pattern_matching_train_0774
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 4, p: 1, y: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.71
math
combinatory_pattern_matching_train_0775
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 2, k: 6}, what is the expected number of times the pattern 'x+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.71
math
combinatory_pattern_matching_train_0776
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {t: 3, u: 1, b: 3} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.43
math
combinatory_pattern_matching_train_0777
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {o: 1, x: 1, z: 2, p: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'o*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.48
math
combinatory_pattern_matching_train_0778
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, p: 2, h: 1, s: 2}. What is the expected number of occurrences of the pattern 's.*j' 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_0779
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {e: 1, r: 1, y: 1, p: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'rp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.23
math
combinatory_pattern_matching_train_0780
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {m: 2, t: 1, j: 3} to form a word, what is the expected number of matches of the pattern 'jm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.7
math
combinatory_pattern_matching_train_0781
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {m: 2, p: 1, d: 2, j: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'hd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.24
math
combinatory_pattern_matching_train_0782
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {c: 3, x: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'rx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
math
combinatory_pattern_matching_train_0783
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {p: 2, o: 1, f: 2, z: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'fz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.24
math
combinatory_pattern_matching_train_0784
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {i: 3, x: 2, k: 2}. What is the expected number of occurrences of the pattern 'x.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.86
math
combinatory_pattern_matching_train_0785
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, d: 1, c: 5}, what is the expected number of times the pattern 'cd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.18
math
combinatory_pattern_matching_train_0786
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {d: 1, j: 3, e: 1, t: 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}" } ]
2.3
math
combinatory_pattern_matching_train_0787
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {t: 1, e: 6}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
4.29
math
combinatory_pattern_matching_train_0788
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, v: 1, n: 2, y: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.2
math
combinatory_pattern_matching_train_0789
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {u: 1, o: 3, q: 3, f: 1} to form a word, what is the expected number of matches of the pattern 'qf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.16
math
combinatory_pattern_matching_train_0790
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {m: 2, n: 1, p: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'n*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.29
math
combinatory_pattern_matching_train_0791
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 3 letters from the multiset {a: 2, i: 1, k: 1, p: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'ip*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.53
math
combinatory_pattern_matching_train_0792
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {z: 2, e: 3, m: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'mz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.62
math
combinatory_pattern_matching_train_0793
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 1, l: 2, d: 2, w: 1}, what is the expected number of times the pattern 'ld*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.8
math
combinatory_pattern_matching_train_0794
combinatory_pattern_matching
null
[ { "role": "user", "content": "When randomly selecting 4 letters from the multiset {a: 1, w: 1, j: 1, q: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'ka+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.1
math
combinatory_pattern_matching_train_0795
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, j: 2, n: 3, e: 1}. What is the expected number of occurrences of the pattern 'j*n' 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_0796
combinatory_pattern_matching
null
[ { "role": "user", "content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, g: 4}. What is the expected number of occurrences of the pattern 'dg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
1.33
math
combinatory_pattern_matching_train_0797
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, m: 2, q: 1, x: 1, k: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.0
math
combinatory_pattern_matching_train_0798
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 4, i: 2}, what is the expected number of times the pattern 'il*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
2.67
math
combinatory_pattern_matching_train_0799
combinatory_pattern_matching
null
[ { "role": "user", "content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, l: 3, x: 1}, what is the expected number of times the pattern 'x+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" } ]
0.13
math