# Chapter 13 - Voting and Apportionment - 13.1 Voting Methods - Exercise Set 13.1: 19

If there are five candidates, 10 comparisons must be made.

#### Work Step by Step

Suppose that the pairwise comparison method is used to determine the winner in an election. In an election with $n$ candidates, the number of comparisons, C, that must be made is determined by the formula $C = \frac{n~(n-1)}{2}$ We can find how many comparisons must be made if there are five candidates. In this case, $n=5$. $C = \frac{n~(n-1)}{2}$ $C = \frac{5~(5-1)}{2}$ $C = 10$ If there are five candidates, 10 comparisons must be made.

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