Question

A pizza shop offers 19 different toppings and offers a discount if 3 toppings are chosen for a pizza. In how many different ways can 3 toppings be chosen?

Answer 1

969

Explanation:

This is a combination question (we don't care in what order the toppings are picked). The general formula for a combination is:

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

We have `n=19 and k=3`:

`C_(19,3)=(19!)/((3!)(16!))=(19xx18xx17)/6=969`