Challenging Permutation question 5

A tennis club has n male players and n female players. For a tournament the players are to be arranged in n pairs, with each pair consisting of one male and one female. Find the number of possible pairings.

Answer: n!

Solution

Suppose the male got to choose his partner. The first male can choose from n females. After he has chosen, the next male can choose from (n-1) females. So the number of possible pairings is n.(n-1).(n-2)…1 = n!

For instance there are 2 male players (M1, M2) and 2 female (F1, F2) players.

One way to arrange 2 pairs of players: M1 F1 and M2 F2

Second way to arrange 2 pairs of players: M1 F2 and M2 F1

Number of ways to arrange 2 pairs of players is 2!

Comments

Some students will give the wrong answer n x n, which is the number of ways to choose a pair.

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