Question

There are 7 females and 8 males. In how many ways can they be chosen for a 4 place group? (I have a test 4th hour and I’m really confused!)

Answer 1

With the added condition of having exactly two females and two males:

There are 7 females to choose from, and 8 males to choose from. So the total number of 4-person groups is

$\dbinom72\dbinom82=\dfrac{7!}{2!(7-2)!}\dfrac{8!}{2!(8-2)!}=21\cdot28=336$