Page 200 - Math Course 3 (Book 2)

Counting Outcomes
Mo. 12

Lesson 5 Key Concept

KEY CONCEPTS: Fundamental Counting Principle

1. Count outcomes using a tree diagram. If an event M can occur in m ways and is followed
2. Count outcomes using the Fundamental by an event N that can occur in n ways, then the
Counting Principle. event M followed by event N can occur in m • n
3. Count outcomes using factorials to solve ways.
a problem.
Words The expression n!, read n factorial,
where n is greater than zero, is the
product of all positive integers begin-
MO. 12 - L5a ning with n and counting backward to 1.
Symbols n! = n • (n – 1) • (n – 2) • ... • 3 • 2 • 1
Tree Diagram and Fundamental Example 5! = 5 • 4 • 3 • 2 • 1 or 120

Counting Principle

By definition, 0! = 1.
Vocabulary A-Z

Let us learn some vocabulary

Jersey Pants Shoes Outcomes Let’s Begin
Black RGB
Gray
Red White RGW
Black
RBB
Black Tree Diagram
White RBW
tree diagram Example
One method used for counting the number of
possible outcomes is to draw a tree diagram.
At football games, a student concession stand
sample space sells sandwiches on either wheat or rye bread. The
The list of all possible outcomes is called the sandwiches come with salami, turkey, or ham, and
sample space. either chips, a brownie, or fruit. Use a tree diagram
to determine the number of possible sandwich
combinations.
event
any collection of one or more outcomes in the
sample space is called an event.

Fundamental Counting Principle

If an event M can occur in m ways and is followed
by an event N that can occur in n ways, then the
event M followed by event N can occur in m • n
ways.

If the team can choose from 3 different colored
jersey, 2 different colored pants, and 2 different
colored pairs of shoes, there are 3 • 2 • 2, or 12,
possible uniforms.

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