Answer
There are 512 different variations available for ordering a pizza.
Work Step by Step
{beef, ham, mushrooms, sausage, peppers, pepperoni, olives, prosciutto, onion}
A pizza can be ordered with any combination of the given toppings, including none or all the toppings. This makes the number of different variations equal to the number of subsets of the given set.
A set of $n$ elements has $2^n$ subsets; therefore, our set has:
$2^9=512$ subsets.
There are 512 different variations available for ordering a pizza.
