#### Answer

$6840$ 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 preference) is important, so we count permutations of r=3 movies taken from n=20.
The formula ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$ applies.
${}_{20}P_{3}=\displaystyle \frac{20!}{17!}=20\times 19\times 18=$
$=6840$ ways