## Thinking Mathematically (6th Edition)

$6840$ ways
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 ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$. ---------------- 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