In a mixed doubles match, how many ways can teams be formed from 5 men and 4 women?

To determine how many ways teams can be formed in a mixed doubles match from 5 men and 4 women, we need to form two teams, each consisting of one man and one woman.

First, we need to select one man from the 5 available men. There are 5 possible choices for the man. Next, we select one woman from the 4 available women. There are 4 possible choices for the woman.

To find the total number of ways to form one team of a man and a woman, we multiply the number of choices for men by the number of choices for women:

5 (choices for men) x 4 (choices for women) = 20 ways to form one team.

Since this scenario involves mixed doubles, we can form two teams in the following manner:

1. Choose 2 men from the 5 available.

2. Choose 2 women from the 4 available.

First, we will select two men from the five. This is calculated using combinations, represented mathematically as 5 choose 2, which is calculated as follows:

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\binom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{5!