## Thinking Mathematically (6th Edition)

The number of permutations possible if $r$ items are taken from $n$ items is ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$. --------------- Sample answer: "How many different 5-digit numbers can be written using 1, 2, 3, 4, and 5?" ${}_{5}P_{5}=\displaystyle \frac{5!}{(5-5)!}=\frac{5!}{0!}=5!$