Question

${}^{10}{P}_r=5040$

Find value of r .

Answer 1

Given that,

${}^{10}{p}_r=5040$

$\frac{10!}{(10-r)!}=5040$

$Weknow10!=5040,$

$(10-r)!=1\Rightarrow (10-r)!=1!or0!$

$(10-r)!=(10-9)!or(10-10)!$

On comparing, we get

Hence, $r=9or10.$