Question

If ${}^{10}{P}_r=5040$ , find the value of $r.$

Answer 1

${}^{10}{P}_r=5040$
$\Rightarrow \frac{10!}{(10-r)!}=10\times 504$
$\Rightarrow \frac{10!}{(10-r)!}=10\times 9\times 8\times 7$
$\Rightarrow \frac{10!}{(10-r)!}=\frac{10!}{6!}$
$\Rightarrow (10-r)!=6!\Rightarrow 10-r=6$
$\Rightarrow r=4$