There are 18 people in a club. The club needs to create a committee of 4 people to plan a party. In how many ways can this be done?

Question

There are 18 people in a club. The club needs to create a committee of 4 people to plan a party. In how many ways can this be done?

Answer 1

This is a combination because the order does not matter, i.e. Joe, John, Jack, and Josh is the same committee as

John, Joe, Josh, and Jack.

 

₁₈C₄ = 18 · 17 · 16 · 15 / 4 · 3 · 2 · 1

₁₈C₄ = 3060

 

Three thousand sixty different committees could be selected.