Question

Pine Pizza Palace sells pizza plain or with one or more of the following toppings: pepperoni, sausage, mushrooms, olives,onions, or anchovies. (six toppings or plain) How many different pizzas can be made? (Hint: A person can select or not select each item.)

Answer 1

six toppings means that there are 2^6=64 ways to select them or not.

Answer 2

number of subsets of 6 elements
= 2^6
= 64

which includes the nullset (plain pizza) and all elements ("the works")