Answer
$_5P_2=20$
Work Step by Step
Using $
_nP_r=\dfrac{n!}{(n-r)!}
$ or the Permutation of $n$ taken $r,$ the given expression, $
_5P_2
,$ is equivalent to
\begin{align*}\require{cancel}
&
\dfrac{5!}{(5-2)!}
\\\\&=
\dfrac{5!}{3!}
\\\\&=
\dfrac{5(4)(3!)}{3!}
\\\\&=
\dfrac{5(4)(\cancel{3!})}{\cancel{3!}}
\\\\&=
5(4)
\\&=
20
.\end{align*}
Hence, $
_5P_2=20
.$
