Lesson 11.6 – 11.7 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.

𝑛! What is n-factorial? 4!=4∙3∙2∙1 The product of the integers from 1 to n. 𝑛! 4!=4∙3∙2∙1

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?

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?

Judges at a science fair are awarding prizes to the first, second, and third-place finishers. The science fair has 10 contestants. How many different ways can the first, second, and third-place prizes be awarded?

You have four posters to hang in your room You have four posters to hang in your room. You want to put one poster on each wall. How many ways can you arrange the posters?

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?

You garage door has a keypad that can be used to open the garage door You garage door has a keypad that can be used to open the garage door. The code has five digits. You remember that the five digits are 1, 3, 5, 7, and 9, but you cannot remember the sequence. What is the probability that you open the garage door on the first try?

Don buys four science fiction books and puts them on his bookshelf side-by-side in random order. What is the probability that they are in alphabetical order by title from left to right?

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.

A basketball league has 5 teams A basketball league has 5 teams. Two of the teams are chosen to play one another. How many different possible matchups are there?

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?

You need to write 4 book reports for your English class You need to write 4 book reports for your English class. Your teacher gives the class a list of 7 books from which to choose. How many different groups of 4 books can you choose from the list?

A credit card company offers its users 3 free magazine subscriptions from a selection of 30 magazines. How many different combinations of 3 magazines can you choose?

You have 10 marbles in a bag You have 10 marbles in a bag. Each marble is a different color, including red, blue, and green. You draw 3 marbles at random. Find the probability that you draw a red, a blue, and a green marble.

A radio station takes the names of the first 20 listeners who call in after hearing a certain song. The station will randomly select 3 of the callers to win tickets to a concert. If 3 friends are among the first 20 callers, what is the probability that the 3 friends will win tickets?

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?