Question

If $2P(5,3)=P(n,4)$ find $n$

Answer 1

Given that:

$2P(5,3)=P(n,4)$

$\frac{2\times 5!}{(5-3)!}=\frac{n!}{(n-4)!}$

$n(n-1)(n-2)(n-3)=5(5-1)(5-2)(5-3)$

On comparing, we get

$n=5$

Hence, this is the answer.