Answer
$_9P_4=3,024$
Work Step by Step
Using $_nP_r=\dfrac{n!}{(n-r)!},$ then the value of the given expression, $
_9P_4
,$ is
\begin{align*}\require{cancel}
&
\dfrac{9!}{(9-4)!}
\\\\&=
\dfrac{9!}{5!}
\\\\&=
\dfrac{9(8)(7)(6)(5!)}{5!}
\\\\&=
\dfrac{9(8)(7)(6)(\cancel{5!})}{\cancel{5!}}
\\\\&=
9(8)(7)(6)
\\&=
3024
.\end{align*}
Hence, $
_9P_4=3,024
.$
