Thread: Probability/Combinations - Question

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

no answer for this question. Could someone please help?


d) there must be at least 3 women and at least 2 men

my answer: (25 3) (25 7-2)
= 25 Cr 3 x 25 Cr 7-2
= 1,105,598,500

Is this correct?

Hello, cnmath16!

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.

There are: . possible committees.

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.

d) there must be at least 3 women and at least 2 men.

There are three cases: .

. .


Answer: . committees.