The Fundamental Counting Principle

In working with probability it is important to be able to count the number of times an event or sequence of events occurs. In some instances counting the number of times an event occurs is obivious. However, there are many situations in which the number of times an event or sequence of events occurs is not obvious. It is in these situations that we use the
Fundamental Counting Principle or Rule.

The trick to using the Fundamental counting rule is to break a task into a sequence of smaller tasks or events. For example:

Suppose a student wanted to purchase a computer system which consists of :

CPU
printer
monitor
keyboard.

Suppose there

4 choices for CPU
5 choices for printer
8 choices for monitor
7 choices for keyboard

How many different computer systems can the student choose from if he has to select one of each item listed?

The solution: Break the task of choosing a computer system into smaller task or events:

Event A: select a CPU.............4 choices
Event B: select a printer...........5 choices
Event C: select monitor............8 choices
Event D: select a keyboard...... 7 choices

Using the fundamental counting principle the answer is: 4 x 5 x 8 x 7 = 1120 different computer systems to choose from.