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?

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

1 - 15

2 - 17

3 - 18

4 - 19

5 - 20