Question

A textbook search committee is considering 18 books for possible adoption. The committee has decided to select 4 of the 18 for further consideration. In how many ways can it do so?

Answer 1

This is a combination problem, since order does not matter. Specifically, it is an 18- choose - 4.
₁₈C₄ = 18! ÷ (4!(18-4)!
= 18! ÷ (4! (14!)) The 14! cancels out in the numerator/denominator
= 18 x 17 x 16 x 15 ÷ (4 x 3 x 2)
= 3,060