Choosing captains

Question

A track team has 8 senior boys and 10 senior girls. How many ways can 2 boy captains and 2 girl captains be selected?

Answer 1

We have to determine whether or not these are permutations or combinations.

Since it doesn't matter which order the captains are chosen, these are combinations.

Combination for the boy captains:

We are choosing 2 captains out of a group of 8 senior boys, so we use

₈C₂ = 28

Combination for the girl captains:

We are choosing 2 captains out of a group of 10 senior girls, so we use

₁₀C₂ = 45

So altogether, after adding 28 and 45, there are 73 different ways to choose 2 boy captains and 2 girl captains from a group of 8 boys and 10 girls