Question

If ${{}^{n}P}_4=5\left({{}^{n}P}_3\right)$, then the value of $n$ is equal to

• A. $5$
• B. $6$
• C. $7$
• D. $8$
• E. $9$

Answer 1

The correct option is D $8$

Given, ${{}^{n}P}_4=5\left({{}^{n}P}_3\right)$
$\Rightarrow \frac{n!}{(n-4)!}=\frac{5\times n!}{(n-3)!}$
$\Rightarrow n-3=5\Rightarrow n=8$