Hello, cnmath16!

There are: . possible committees.A club consists of 25 married couples.

Determine how many ways a committee of 7 people can be formed from these couples if:

c) at least one person must be a man.

The opposite of "at least one man" is "no men" (all women).

There are: . all-women committees.

. . Hence, the rest must contain at least one man.

Answer: . committees with at least one man.

There are three cases: .d) there must be at least 3 women and at least 2 men.

. .

Answer: . committees.