Question

A batsman can score $0,1,2,3,4$ or $6$ runs from a ball. The number of different sequences in which he can score exactly $30$ runs in an over of six balls, is

• A. $4$
• B. $71$
• C. $56$
• D. $76$

Answer 1

Answer: (B)

$71$

Score $=0,1,2,3,4$ or $6$ from a ball
Number of different sequences in which he can score exactly $+30$ runs in an over of $6$ balls is

Possibilities Permutations
$6,6,6,6,6,0$ $\frac{6!}{5!}=6$
$6,6,6,6,4,2$ $\frac{6!}{4!}=30$

$6,6,6,6,3,3$ $\frac{6!}{4!2!}=15$

$6,6,6,4,4,4$ $\frac{6!}{3!3!}=20$

Total ways $=6+30+15+20$
$=71$