Lesson 13.3

The Counting Principle

Essential Question: How do you use the counting principle to count

outcomes?

Before we start…

Your closet contains a red shirt, a green shirt, a blue shirt, a pair of jeans, a pair of corduroys, a pair of sneakers, and a pair of boots. How many different outfits of a shirt, pants, and shoes can be made? Make a tree diagram to show your results.

What is the Counting Principle?

A method for determining how many different ways you can choose an event

The Counting Principle

If one event can occur in m ways, and for each of these a second event can occur in n ways, then the number of ways that the two events can occur together is .

The counting principle can be extended to three or more events.

How do you use the counting principle to determine the number of outcomes?

Find the product of the number of outcomes for each event in an experiment.

Track Events A track meet has 6 running events, 3 throwing events, and 2 relay events. You want to complete in one running event, one throwing event, and one relay event. How many different choices do you have for competing in one of each type of event?

License Plates The standard New York state license plate has 3 letters followed by 4 digits. How many different license plates are possible if the digits and letters can be repeated?

Number Cubes You roll a green number cube, a red number cube, and a blue number cube. How many outcomes are possible?

Lunch You can choose from 4 salads and 6 dressings. You can add chicken, shrimp, or neither. Find the number of different salad choices using the counting principle.

Office Supplies You have 8 kinds of writing paper and 5 envelope colors. How many pairings of one kind of writing paper and one envelope color are possible?

Passwords You are assigned a computer-generated 4-digit password to access your new voice mail account. If the digits can be repeated, what is the probability that your assigned password is 1234?

Number Cubes You roll a green number cube, a blue number cube and a red number cube. What is the probability that the green number cube is a 2, the red number cube is a 6, and the blue number cube is a 3?

How do you use the counting principle to count outcomes?

Ticket Out the DoorYour class is having an election. There are 3 candidates for president, 5 for vice president, 2 for secretary, and 6 for treasurer. How many different groups of winning candidates can be chosen?