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 = 71Related Questions on Permutation and Combination
A. 3! 4! 8! 4!
B. 3! 8!
C. 4! 4!
D. 8! 4! 4!
A. 7560,60,1680
B. 7890,120,650
C. 7650,200,4444
D. None of these
A. 8 × 9!
B. 8 × 8!
C. 7 × 9!
D. 9 × 8!
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