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

Answer: Option B

Solution(By Examveda Team)

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