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?

1 - 15

2 - 17

3 - 18

4 - 19

5 - 20

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