Merging two round-robins

EasyCombinatorics~3m

Two chess clubs each ran an internal round-robin (every member played every other member once). Club A played $15$ games and Club B played $21$ games. The clubs then merge, and every Club-A member plays every Club-B member exactly once. How many of these new cross-club games are played?

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Solve $\binom{a}{2}=15$ and $\binom{b}{2}=21$ for the club sizes first.
Cross-club games are the product $a\cdot b$ , not $\binom{a+b}{2}$ .

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Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude

Merging two round-robins

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