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1. In a cricket match if a batsman score 0, 1, 2, 3, 4 or 6 runs of a ball, then find the number or different sequences in which he can score exactly 30 runs of an over. Assume that an over consists of only 6 balls and there were no extra and no run outs.

A. 86

B. 71

C. 56

D. 65

Solution:

Case A: Five 6 and one 'zero' =

\frac{6!}{5!}

= 6
Case B: Four 6 and one '2' and one '4' =

\frac{6!}{4!}

= 30
Case C: Three 6 and three '4' =

\frac{6!}{3! \times 3!}

= 20
Case D: Four 6 and two '3' =

\frac{6!}{4! \times 2!}

= 15
Total number of different sequences = 71

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