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There are 5 girls and 5 boys in a chess club. The club holds a round-robin tournament in which every player plays against every other player exactly once.  How many games are payed in total?

 Apr 4, 2021
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Forget about the girl/boy condition. We simply choose $2$ players from a group of 10, so the answer is $\binom{10}{2}=\boxed{45}$.

 Apr 4, 2021

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