Answer
$6840$
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 three films, thus we have to use permutations. We have $20$ films for $3$ spots, thus $_{20}P_{3}=\frac{20!}{(20-3)!}=20\cdot19\cdot18=6840$
