11-7 Permutations Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Warm Up 1. How many 2-side-dish meals can be made from 6 choices of side dishes? 2. Kim has shorts in blue, black, and tan. She has shirts in blue, yellow, red, and green. How many different combinations can she make? 3. If you go to the movies and are allowed to get 2 snacks and there are 9 snacks to choose from, how many combinations are there to pick from? Course Permutations

Problem of the Day Replace each ? with a different digit from 1 through 9 to make a proportion. (Hint: The digits are not being multiplied.) Possible answer: ?? = = Course Permutations

Learn to find the number of possible permutations. Course Permutations

Vocabulary permutation factorial Insert Lesson Title Here Course Permutations

An arrangement of objects or events in which the order is important is called a permutation. You can use a list to find the number of permutations of a group of objects. Course Permutations

In how many ways can you arrange the letters, A, B, and T ? Additional Example 1: Using a List to Find Permutations Use a list to find the possible permutations. There are 6 ways to order the letters. A, B, TB, A, TT, A, B A, T, BB, T, AT, B, A Course Permutations

Check It Out: Example 1 Insert Lesson Title Here In how many ways can you arrange the colors red, orange, blue? Use a list to find the possible permutations. There are 6 ways to order the colors. red, orange, blue red, blue, orange orange, red, blue orange, blue, red blue, orange, red blue, red, orange Course Permutations List all permutations beginning with red, then orange, and then blue.

You can use the Fundamental Counting Principle to find the number of permutations. Course Permutations

Mary, Rob, Carla, and Eli are lining up for lunch. In how many different ways can they line up for lunch? Once you fill a position, you have one less choice for the next position. Additional Example 2: Using the Fundamental Counting Principle to Find the Number of Permutations There are 4 choices for the first position. There are 3 remaining choices for the second position. There are 2 remaining choices for the third position. There is one choice left for the fourth position. 4 · 3 · 2 · 1 There are 24 different ways the students can line up for lunch. Multiply.= 24 Course Permutations

Course Permutations The Fundamental Counting Principle states that you can find the total number of outcomes by multiplying the number of outcomes for each separate experiment. Remember!

Check It Out: Example 2 How many different ways can you rearrange the letters in the name Sam? Once you fill a position, you have one less choice for the next position. Insert Lesson Title Here There are 3 choices for the first position. There are 2 remaining choices for the second position. There is one choice left for the third position. 3 · 2 · 1 There are 6 different ways the letters in the name Sam can be arranged.. Multiply.= 6 Course Permutations

A factorial of a whole number is the product of all the whole numbers except zero that are less than or equal to the number. “3 factorial” is 3! = 3 · 2 · 1 = 6 “6 factorial” is 6! = 6 · 5 · 4 · 3 · 2 · 1 = 720 You can use factorials to find the number of permutations. Course Permutations

How many different orders are possible for Shellie to line up 8 books on a shelf? Additional Example 3: Using Factorials to Find the Number of Permutations Number of permutations = 8! = 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1 = 40,320 There are 40,320 different ways for Shellie to line up 8 books on the shelf. Course Permutations

Check It Out: Example 3 Insert Lesson Title Here How many different orders are possible for Sherman to line up 5 pictures on a desk? Number of permutations = 5! = 5 · 4 · 3 · 2 · 1 = 120 There are 120 different ways for Sherman to line up 5 pictures on a desk. Course Permutations

Lesson Quiz 1. In how many different ways can Anna, Barbara, and Cara sit in a row? 3. In how many different ways could 4 people enter a roller-coaster car? 4. How many different orders are possible for 6 basketball players to sit on the bench while waiting to be announced at the beginning of a game? 6 Insert Lesson Title Here Course Permutations