A club has 24 male and 24 female members. The club is choosing a committee of 44 members. The committee must have 24 male and 20 female members. How many different committees can be choosen?
+36916 How many ways can you choose 20 females out of a pool of 24 ? 24 c 20 = 10626
24 males out of a pool of 24 ? 24 c 24 = 1 (duh !)
10626 ways
+36916 How many ways can you choose 20 females out of a pool of 24 ? 24 c 20 = 10626
24 males out of a pool of 24 ? 24 c 24 = 1 (duh !)
10626 ways
+2862 Ignore the statement "the club is choosing a committee of 44 members"
We already have "24 male and 20 female members"
Since we have 24 male members in the club, we only need to worry about female members.
So how many ways can we choose 20 out of 24?
24!/(4!)(20!) = 10626
