6th Grade Math Textbook, Fundamentals

 &KDSWHU

12-2

Key Concept

If an event can occur in mways and a second event can occur in nways, then the

total number of possible ways that the events can occur together equals m• n.

This principle can be extended to any number of events.

Fundamental Counting Principle

Fundamental Counting Principle

and Factorials

Objective To use the Fundamental Counting Principle to find the size of a

sample space • To use factorials to find the size of a sample space

A diner offers a variety of made-to-order
sandwiches. Customers can choose from rye (R)
or wheat (W) bread; grilled chicken (G) or
turkey (T); and Swiss (S), cheddar (C), or American (A)
cheese. On her first day of work at the diner, Althea wants
to determine how many different kinds of sandwiches
she might be asked to make.

To find the total number of different kinds of sandwiches,

Althea can draw a tree diagram or use multiplication.

Method 1 Make a Tree Diagram

Swiss

Cheddar

American

Grilled Chicken

Turkey

Rye

Swiss

Cheddar

American

Swiss

Cheddar

American

Grilled Chicken

Turkey

Wheat

Swiss

Cheddar

American

Sample space {(R, G, S); (R, G, C); (R, G, A); (R, T, S); (R, T, C); (R, T, A);

(W, G, S); (W, G, C); (W, G, A); (W, T, S); (W, T, C); (W, T, A)}

There are 12 elements in the sample space.

Method 2 Use Multiplication

bread meat cheese

choices choices choices

Total kinds of sandwiches  2 • 2 • 3  12

So Althea might be asked to make any one of 12 different kinds of sandwiches.

Using multiplication to find the sample space is known as the

Fundamental Counting Principle.