Answer
$_4P_4=24$
Work Step by Step
Using $
_nP_r=\dfrac{n!}{(n-r)!}
$ or the Permutation of $n$ taken $r,$ the given expression, $
_4P_4
,$ is equivalent to
\begin{align*}\require{cancel}
&
\dfrac{4!}{(4-4)!}
\\\\&=
\dfrac{4!}{0!}
\\\\&=
\dfrac{4!}{1}
&\text{(use }0!=1)
\\\\&=
4!
\\&=
4(3)(2)(1)
\\&=
24
.\end{align*}
Hence, $
_4P_4=24
.$
