Question

If ${}^n{P}_r=720$ and ${}^n{C}_r=120$, find the value of r.

Answer 1

We know that,
${}^n{P}_r=720{=}^n{C}_r$

$\Rightarrow r!=\frac{{}^n{P}_r}{{}^n{C}_r}=\frac{720}{120}=6\Rightarrow r!=6$

$\Rightarrow r!=3\times 2\times 1\Rightarrow r!=3!\Rightarrow r=3$