Question

The student council consists of four boys and six girls. How many
on a committee of five council members are possible if:

(a) There are no restrictions?
(b) The committee must have at least two girls.

Answer 1

a) there are 10 students to choose from, you want to choose any 5
number = C(10,5)
= ...

(I assume you know that C(10,5) = 10!/(5!5!) )

b) what you don't want is : number with no girls + number with 1 girl
but ... since there are only 4 boys and you want 5 members, the case of no girls is not possible and you must choose 1 girl.
number of cases with 1 girl = C(4,4)*C(6,1) = 6

the number of committees with at least 2 girls
= C(10,5) - 6 = ....