Answer
$_7P_4=840$
Work Step by Step
Using $
_nP_r=\dfrac{n!}{(n-r)!}
$ or the Permutation of $n$ taken $r,$ the given expression, $
_7P_4
$ is equivalent to
\begin{align*}\require{cancel}
_7P_4&=
\dfrac{7!}{(7-4)!}
\\\\&=
\dfrac{7!}{3!}
\\\\&=
\dfrac{7(6)(5)(4)(\cancel{3!})}{\cancel{3!}}
\\\\&=
7(6)(5)(4)
\\&=
840
.\end{align*}
Hence, $
_7P_4=840
.$
