## Thinking Mathematically (6th Edition)

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 nine candidates. In this case, $n=9$. $C = \frac{n~(n-1)}{2}$ $C = \frac{9~(9-1)}{2}$ $C = 36$ If there are nine candidates, 36 comparisons must be made.