Answer
The male actors can be selected in 116,280 ways for four roles.
Work Step by Step
We know that the order in which the four actors are selected makes a difference as the all the actors would be cast for a different role.
Since the order matters, we use permutations.
The four officers are to be selected from a club of twenty members. So, $ n=20,r=4$.
Hence,
$\begin{align}
& _{20}{{P}_{4}}=\frac{20!}{\left( 20-4 \right)!} \\
& =\frac{20!}{16!} \\
& =\frac{20\times 19\times 18\times 17\times 16!}{16!} \\
& =116,280
\end{align}$
