Algebra 1 Notes:

Probability Part 2:Counting Outcomes

Objectives

• Calculate the number of possible outcomes using the fundamental counting principle

Take A Guess

How many different ways can I line up 8 students for

a picture?

Example 1

At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.

Example 1

At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.

Example 1 Bread

Example 1 Bread

wheat

rye

Example 1 Bread Meat

wheat

rye

Example 1

At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.

Example 1

At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.

Example 1 Bread Meat

salami

wheat

turkey ham

rye

Example 1 Bread Meat

salami

wheat

turkey ham

salami

rye turkey

ham

Example 1 Bread Meat Side Item

salami

wheat turkey

ham salami

rye turkey

ham

Example 1

At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.

Example 1

At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.

Example 1 Bread Meat Side Item

chips salami brownie

fruit wheat

turkey ham

salami

rye turkey

ham

Example 1 Bread Meat Side Item Outcomes

chips 1 salami brownie 2

fruit 3 wheat

turkey ham

salami

rye turkey

ham

Fundamental Counting Principle

Multiply the number of ways EACH event can occur.

Example 1

At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.

Breads Meat Side Total

2 x 3 x 3 =

Breads Meat Side Total

2 x 3 x 3 = 18

Example 2The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order?hard drive choices

11

Example 2The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order?hard drive keyboard choices choices

11

Example 2The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order?hard drive keyboard choices choices

11 6

Example 2The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order?hard drive keyboard mouse choices choices choices

11 6

Example 2The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order?hard drive keyboard mouse choices choices choices

11 6 4

Example 2The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order?hard drive keyboard mouse monitor choices choices choices choices

11 6 4

Example 2The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order?hard drive keyboard mouse monitor choices choices choices choices

11 6 4 4

Example 2The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order?hard drive keyboard mouse monitor choices choices choices choices

11 • 6 • 4 • 4

Example 2The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order?hard drive keyboard mouse monitor choices choices choices choices

11 • 6 • 4 • 4 = 1,056

Example 2The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order?hard drive keyboard mouse monitor choices choices choices choices

11 • 6 • 4 • 4 = 1,056 different computers

Vocabulary

Factorial – A number multiplied by every positive integer less than itself

Looks like an exclamation point.

Example 3There are 8 students in the Biology Club at Central High School. The students want to stand in line for their yearbook picture. How many different ways could the 8 students stand for their picture?

Example 3There are 8 students in the Biology Club at Central High School. The students want to stand in line for their yearbook picture. How many different ways could the 8 students stand for their picture?

8 • 7 • 6 • 5 • 4 • 3 • 2 • 1

Example 3There are 8 students in the Biology Club at Central High School. The students want to stand in line for their yearbook picture. How many different ways could the 8 students stand for their picture?

8 • 7 • 6 • 5 • 4 • 3 • 2 • 1 = 8!

Example 3There are 8 students in the Biology Club at Central High School. The students want to stand in line for their yearbook picture. How many different ways could the 8 students stand for their picture?

8 • 7 • 6 • 5 • 4 • 3 • 2 • 1 = 8! = 40,320

40,320 ways they could stand

Homework

Worksheet:

Counting Outcomes