Question

An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3 person committee be created if the committee must include the male employee?

Answer 1

We can approach this as how many 2 person female committees can we make that we can add the male to.

5 C 2 (combinations of 5 taken 2 at a time order doesn't matter)

5 x 4 = 20 = 10 ways. Since the male can join any of the groups there are
2 x 1 2 still 10 ways.

Here's another way of looking at it. Let's call the five females A, B, C, D and E

Here are the pairings:
AB BC CD DE
AC BD CE
AD BE
AE The male can be the 3rd person in any group. Once
again, there are 10 ways to do this.