EXAMPLE 1.6.15

Pizza Shack is offering the following special deal this month: for one low price ($6.99) you can get a large pizza with up to 4 different toppings. There are 8 toppings from which to choose. How many different topping combinations are possible?

A. 70

B. 1680

C. 163

D. 32

SOLUTION

In this case, "up to 4 different toppings" means either 0 toppings or 1 topping or 2 toppings or 3 toppings or 4 toppings.

Number of ways to choose 0 toppings: C(8,0) = 1

Number of ways to choose 1 topping: C(8,1) = 8

Number of ways to choose 2 toppings: C(8,2) = 28

Number of ways to choose 3 toppings: C(8,3) = 56

Number of ways to choose 4 toppings: C(8,4) = 70

The total number of possibilities is:

1 + 8 + 28 + 56 + 70 = 163