# Chapter 11 - Counting Methods and Probability Theory - 11.2 Permutations - Exercise Set 11.2 - Page 701: 61

Sample answer: "How many different 5-digit numbers can be written using 1, 2, 3, 4, and 5?"

#### Work Step by Step

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?" ${}_{5}P_{5}=\displaystyle \frac{5!}{(5-5)!}=\frac{5!}{0!}=5!$

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