Question

In how many ways can a committee of two men and two women be formed from a group of nine men and nine women?

Answer 1

Answer:  1296 different committees

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Explanation:

We have 9 men and we want to select 2 of them. The order doesn't matter. If order did matter, then we would have 9*8 = 72 permutations. Since order doesn't matter, we have instead 72/2 = 36 combinations. The reason why order doesn't matter is because no person outranks another on a committee. Any given seat is the same as anyone else. This is excluding any chairperson of course.

So we have 36 ways to select the men. There are also 36 ways to select the women as well for the exact same steps as listed above. This is due to there being 9 women total and we're selecting 2 of them.

Since there are 36 ways to select the two men, and 36 ways to select the two women, this leads to a total of 36*36 = 1296 different committees

It might help to think of a table that has 36 rows and 36 columns. Each row could represent a different two-person group of men while each column represents a different two-person group of women. The intersection of a given row and column would then form a unique four-person committee. So that may help visually show why there are 36*36 = 1296 different committees (each committee is an inner cell).