Question

A pizza place offers 5 different cheeses and 10 different toppings. In how many ways can a pizza be made with 2 cheese and 3 toppings?

Answer 1

5C2x10C3 = 1200. Unbelievably!
Given that your not allowed to have the same cheese count twice as your two cheeses and so on.

Explanation:

Let's say you have 5 cheeses A,B,C,D and E

You want to make a combination of 2 cheeses.
These are the possible combinations.
AB, AC, AD, AE, BC, BD, BE, CD, CE, DE.

10 possibilities altogether. You can work the out on the calculator using nCr, so by pressing 5, then nCr, then 2. The answer should be 10.

For each of these 10 cheese combinations, you then have 10C3 choices of toppings. I won't write them all down here as there are 120 combinations of toppings.

You then need to multiply these together to discover how many there are altogether.
10x120 = 1200