Question

A test consists of 20 problems and students are told to answer any 15 of these questions. In how many different ways can they choose the 15 questions?

Answer 1

1 - 15
2 - 17
3 - 18
4 - 19
5 - 20

Answer 2

Since order is not important, we are looking for unique combinations. For this type of problem you use the "n choose k" equation.

n!/(k!(n-k)!), where n=total amount of choices, k=number of choices made.

In this case:

20!/(15!(20-15)!)

20!/(15!*5!)

15504