Answer
$863,040$
Work Step by Step
Using $_nP_r=\dfrac{n!}{(n-r)!},$ the given expression, $
_{32}P_{4}
,$ evaluates to
\begin{array}{l}\require{cancel}
=\dfrac{32!}{(32-4)!}
\\\\=
\dfrac{32!}{28!}
\\\\=
\dfrac{32(31)(30)(29)(\cancel{28!})}{\cancel{28!}}
\\\\=
863,040
\end{array}