Combination or Permutation

Question

From our class, (20 females, 15 males), four students are to be chosen to form a committee. In how many different ways can the student be chosen such that there would be at least one female?

Answer 1

One way would be to find the committees that have 1,  2, 3, or 4 females

This is C(20,1)C(15,3)+C(20,2)C(15,2)+C(20,3)C(15,1)+C(20,4)C(15,0) = 50995

 

The shortcut is to find the ways we can form the committee - the ways that have all males

As there are 35 people altogether, including 15 males, this would be

C(35,4) - C(15,4) = 52360 - 1365 = 50995