EXAMPLE 1.4.6 There are 5 guys on Gomer's bowling team. After the beer frame they will each choose one of the following: Scud, Scud Lite, or Scud Ice. How many outcomes are possible?

A. 60
B. 125
C. 15
D. 243
E. 120

SOLUTION

This process involves 5 decisions, since each member of the bowling team must choose a type of beer.

First person's choice: Scud, Scud Lite, or Scud Ice? 3 options
Second person's choice: Scud, Scud Lite, or Scud Ice? 3 options
Third person's choice: Scud, Scud Lite, or Scud Ice? 3 options
Fourth person's choice: Scud, Scud Lite, or Scud Ice? 3 options
Fifth person's choice: Scud, Scud Lite, or Scud Ice? 3 options

According to the Fundamental Counting Principle the number of outcomes is:
(3)(3)(3)(3)(3) = 3⁵ = 243