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