Lesson 13.3

Find Probabilities Using

Combinations

Essential Question: How do you use combinations to count possibilities?

Before we start…

Suppose Kylie, Alexa, Ben and Marco are in line to ride a roller coaster in which a car has two seats in the front and two seats in the back. What are the different ways the four friends can pair up to ride the roller coaster? (Who sits on the left and who sits on the right does not matter).

What is a combination?

In a drawing for 3 identical prizes, you would use combinations, because the order of the winners would not matter.

A selection of objects in which order is not important.

How do you calculate a combination?

• Calculating a combination can be done 2 ways:

– You can make a list of all the possibilities

– You can use the formula for taking n objects r at a time

How do you calculate the number of combinations of n objects?

You use the formula

Remember n! is n factorial, which is the product of the

integers from 1 to n.

!

! !n rnC

r n r

Count the combinations of 2 letters from the list A, B, C and D.

Count the combinations of 3 letters from the list A, B, C, D and E.

You order a sandwich at a restaurant. You can choose 2 side dishes from a list of 8. How many combinations of side dishes are possible?

You can choose 2 courses out of a list of 6. How many combinations of electives are possible?

For your school picture, you can choose 4 backgrounds from a list of 10. How many combinations of backdrops are possible?

The buyer for a retail store must decide which sweaters to stock for the upcoming

fall season. A sweater from one manufacturer comes in 5 different colors

and 3 different textures. The buyer decides that the store will stock the sweater in 3 different colors and 2 different textures.

How many different sweaters are possible?

The buyer for a sporting goods store must decide which athletic shoes to stock for the upcoming selling season. A shoe from one manufacturer comes in 6 different colors and 4 different styles. The buyer decides that the store will stock the shoes in 4 different colors and 2 different styles. How many different shoe combinations are possible?

• You are ordering a burrito with 2 main ingredients and 3 toppings. The menu below shows the possible choices. How many different burritos are possible?

A yearbook editor has selected 14 photos, including one of you and one of your friend, to use in a collage for the yearbook. The photos are placed at random. There is room for 2 photos at the top of the page. What is the probability that your photo and your friend’s photo are the two placed at the top of the page?

You work 3 evenings each week at a bookstore. Your supervisor

assigns you 3 evenings at random from the 7 possibilities. What is

the probability that your schedule this week includes working on

Friday?

On a television game show 9 members of the studio audience are randomly selected to be eligible contestants.

Six of the 9 eligible contestants are randomly chosen to play a game on stage. How many combinations of 6 players from the group of eligible contestants are possible?

You and your two friends are part of the group of 9 eligible contestants. What is the probability that all three of you are chosen to play the game on stage?

• How do you use combinations to count possibilities?

Ticket Out the Door• You have the first season of your favorite television

show on a set of DVDs. The set contains 13 episodes. You have time to watch 3 episodes. How many combinations of 3 episodes can you watch?