Algebra 2 permutations

Question

There are 16 girls and 20 boys in a class. A team of 3 students is to be selected for preparing a science project from this class. How many ways can at a two boys and a girl be selected from this class?

Answer 1

To form a team, we need to complete two steps: (i) Choose 2 boys out of 20 boys; the number of ways to do so is C(20,2)=(20*19)/2=190. (ii) Choose 1 girl out of 16 girls; the number of ways to do so is C(16,1)=16. So by the multiplicative rule, the number of ways to form a team of 3 persons with 2 boys and 1 girl is equal to 190*16=3040.

Answer 2

How many options for the girl on the team? 16

How many options for the first boy? 20

How many options for the second boy? 20–1 = 19 (we already used one boy of the 20 for the "first boy")

So, the number of options is 16 times 20 times 19. You have a calculator!