Answer
$116280$
Work Step by Step
If we want to choose $k$ elements out of $n$ regarding the order, not allowing repetition, we can do this in $_{n}P_k=\frac{n!}{(n-k)!}$ ways.
The order matters here when choosing the actors, thus we have to use permutations.
We have $20$ people for $4$ spots, thus the number of possibilities is $_{20}P_{4}=\frac{20!}{(20-4)!}=20\cdot19\cdot18\cdot17=116280$
