## Thinking Mathematically (6th Edition)

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 (in which the chosen cars finish) is important, so we count permutations of r=3 cars taken from n=6. The formula ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$ applies. ${}_{6}P_{3}=\displaystyle \frac{6!}{3!}=6\times 5\times 4$ $=$120 ways