The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is:
Solutions · 1
Official solution
Sequentially pairing: for the first team, 15×15 choices; for the second, 14×14; and so on down to 1×1:
\[\sum_{k=1}^{15}k^2 = \frac{15\times16\times31}{6} = 1240\]