Answer to Question #20286 in Combinatorics | Number Theory for Fox Thorpe

Question

A local pizza restaurant has three different crusts and ten different toppings. A “plain” pizza has cheese only.

“Double-toppings” are not allowed; that is, you cannot order "double mushrooms" or "triple jalapenos."

Customers may order any number of toppings from 0 to 10 on any of the three types of crust. How many different pizzas are possible?

Answer 1

There are 3 possible crusts and 10 different toppings. Therefore, there are

N = 3·10 = 30

different possible pizzas with toppings and there are also three types of plain pizza without any topping. So, there are

M = N + 3 = 30 + 3 = 33

different possible pizzas.