Lesson 12.5 – 12.6 Permutations and Combinations Essential Question: How do you use permutations and 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 permutation? An arrangement of objects in which order is important. The 6 possible permutations of the letters A, B and C are: ABC ACB BAC BCA CAB CBA

How do you calculate a permutation? You can use the counting principle, the formula or you can use the nPr button on the calculator. nPr= 𝑛! 𝑛−𝑟 ! n is the number of objects you have to select from and r is the number of objects you choose.

Amusement Parks Yen, Brianna, and Carlos go to an amusement park Amusement Parks Yen, Brianna, and Carlos go to an amusement park. How many ways can they stand in line to buy tickets for the rides?

In how many ways can you arrange all of the letters in the word JULY?

Volleyball There are 8 volleyball teams in a tournament Volleyball There are 8 volleyball teams in a tournament. In how many ways can teams place first, second, third and fourth?

Your band has written 12 songs and plans to record 9 of them for a CD Your band has written 12 songs and plans to record 9 of them for a CD. In how many ways can you arrange the songs on the CD?

Twelve marching bands are entered in a competition Twelve marching bands are entered in a competition. How many ways can first, second, and third place be awarded?

Two students are chosen from a group of 6 to read the first and second poems at the school’s poetry reading. How many different ways can the students be chosen?

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? You can make a list of all the possibilities or you can use the nCr button on the calculator. nCr= 𝑛! 𝑟! 𝑛−𝑟 ! n is the number of objects you have to select from and r is the number of objects you choose.

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

You have 4 tickets to the county fair and can take 3 of your friends You have 4 tickets to the county fair and can take 3 of your friends. You can choose from Abby, Brian, Chloe and David. How many different choices of groups of friends do you have?

You order a sandwich at a restaurant 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?

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

You are shopping at a bookstore. You have enough money to buy 4 books You are shopping at a bookstore. You have enough money to buy 4 books. There are 7 books at the store that you want to read. How many combinations of books can be purchased?

How do you use permutations and combinations to count possibilities? Permutations are used when order is important. Combinations are used when order doesn’t matter.

How do you use permutations and combinations to count possibilities?

Ticket Out the Door How many ways can a judge award first, second and third places at a science fair with 23 entries?