EXAMPLE 1.4.10

Gomer is going to order a frozen tofu cone from I Definitely Believe It's Tofu.

The following toppings are available:

1. carob chips

2. frosted alfala sprouts

3. seaweed sprinkles

4. rolled oats

5. rose hips

He may choose all, some or none of these toppings. How many topping combinations are possible?

A. 5

B. 10

C. 25

D. 32

E. 120

SOLUTION

In choosing some assortment of items, Gomer needs to make five "yes-or-no" decisions:

i. Does he want carob chips? 2 options ("yes" or "no")

ii. Does he want frosted alfala sprouts? 2 options ("yes" or "no")

iii. Does he want seaweed sprinkles? 2 options ("yes" or "no")

iv. Does he want rolled oats? 2 options ("yes" or "no")

v. Does he want rose hips? 2 options ("yes" or "no")

According to the Fundamental Counting Principle the number of outcomes is

(2)(2)(2)(2)(2) = 32.

Notice that this answer is related to a topic from Unit 1 (Set Mathematics). When he chooses an assortment of toppings, he is choosing some subset from the set of five toppings. Recall that if a set has 5 elements, then the number of subsets is 2⁵, or 32. We have actually used the Fundamental Counting Principle to count the number of subsets in a 5-element set.