Round-robin tournament

#tournament#match counting#combination

Statement

In a round-robin tournament with $n$ teams, each pair plays once. How many matches occur?

Hint

Count unordered pairs.

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Count pairs. $\binom{n}{2}=\frac{n(n-1)}{2}$ matches.

Conclusion. $\frac{n(n-1)}{2}$ matches.

Example. $n=8$ : $\frac{8\cdot7}{2}=28$ matches.