Question

If ${}^n{P}_4=20{}^n{P}_2$ find '$n$'

Answer 1

${}^n{P}_4={20}^n{P}_2\Rightarrow \frac{n!}{(n-4)!}=20\frac{n!}{(n-2)!}\Rightarrow (n-3)(n-2)=5\times 4\Rightarrow n=7$

Hence the correct answer is $7$