Answer
$336$ ways
Work Step by Step
A permutation from a group of items occurs when no item is used more than once and the order of arrangement makes a difference.
The number of permutations possible if $r$ items are taken from $n$ items is
${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$.
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Order (of roles which the chosen actors play) is important,
so we count permutations of r=3 actors taken from n=8.
The formula ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$ applies.
${}_{8}P_{3}=\displaystyle \frac{8!}{5!}=8\times 6\times 7$
$=336$ ways