A ballroom dancing class has 20 men and 24 women. Five pairs are to be chosen, each consisting of one man and one woman, and no individual can be included in more than one pair.1 How many different ways can the 5 pairs be chosen?
2026-04-25 17:38:50.1777138730
How many different ways can the 5 pairs be chosen?
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$20 \choose 5$ choices for the $5$ men, $24 \choose 5$ for the women. And there are $5!$ possible orderings for the pairs. Multiplying the three terms gives the answer.