Question

In a shooting competition a man can score $0,2$ or $4$ points for each shot. Then the number of different ways in which he can score $14$ points in $5$ shots, is $N$, then number of digits in $N$' equals.

Answer 1

In the shooting competition, man can score $0,2,or4$

He scored $14$ points in $5$ shots.

No. of ways in which he can do that,

$\Rightarrow 1).4,4,4,2,0=\frac{5!}{3!}=20$

$\Rightarrow 2).2,2,2,4,4=\frac{5!}{3!2!}=10$

$\therefore N=20+10=30$

Hence, the answer is $30.$