# Chapter 11 - 11.6 - Counting Principles - 11.6 Exercises - Page 825: 69

5 diagonals.

#### Work Step by Step

We must select two vertices among five vertices. The order in which they are selected is not important. So, we have $_5C_2$ different combinations: $_5C_2=\frac{5!}{(5-2)!~2!}=\frac{5\times4\times3!}{3!~2!}=10$ But, among those 10 combinations, five are sides. $Diagonals=10-5=5$

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