Question

A pizza place offers 6 different cheeses and 12 different toppings. In how many ways can a pizza be made with 1 cheese and 3 toppings?

Answer 1

You need to "choose" three toppings, which means you need to do a combination (versus a permutation, which would only be needed if you cared about the order that the toppings are added to the pizza, which you obviously don't care about). The combination formula is n!/(r!(n-r)!).
12!/(12-3)!(3!)= 220 ways to choose toppings.
**know that ! Means 12*11*10*9...*3*2*1

Then multiply that by the 6 cheeses to get 220*6 = 1,320 ways. (Each choice of three different toppings can be paired with six different choices for cheese)