Question

A pizza place offers 4 different cheeses and 10 different toppings. In how many ways can a pizza be made with 2 cheese and 3 toppings?

Answer 1

`720` different ways to make a 2-cheese, 3-topping pizza

Explanation:

This is a combinations question - we don't care in what order the toppings and cheeses are put on the pizza - we only care that they are there.

The general formula is:

`C_(n,k)=(n!)/((k!)(n-k)!)` with `n="population", k="picks"`

Cheeses

We want to choose 2 cheeses from the 4 offered:

`C_(4,2)=(4!)/((2!)(2!))=24/(2xx2)=6`

Toppings

We want to choose 3 toppings from the 10 offered:

`C_(10,3)=(10!)/((3!)(7!))=(10xx9xx8)/6=120`

Together

These are independent choices, and so we multiply the results:

`6xx120=720` different ways to make a 2-cheese, 3-topping pizza