1. Review Homework Spongebob Worksheet 스폰지밥 네모바지 스폰지밥

2. Permutations

3. Permutations What is a Permutation? - Have you ever been in an ice cream shop and wondered about all the different ways you could order three different scoops of ice cream? - A PERMUTATION is an arrangement or listing in which order IS important. -the act or process of changing the lineal order of an ordered set of objects -an ordered arrangement of a set of objects

4. Permutations Real World Example: Five students are finalists in the school spelling bee. How many ways can they finish first, second, and third?

5. Permutations Real World Example: Five students are finalists in the school spelling bee. How many ways can they finish first, second, and third? P(5,3) = 5 x 4 x 3 = 60 different ways Also written 5 P 3

6. Permutations How Do I Find The Value of A Permutation? - We calculate the value of a permutation in the following way: P(5,3) = 5 x 4 x 3 = 60 different ways Start with this number Count down this many numbers (1)(2)(3)

7. Permutations Example 1: Permutations. Find the value for P(5,2).

8. Permutations Example 1: Permutations. Find the value for P(5,2). P(5,2) = 5 x 4 = 20 Start with this number We are using this many numbers so we count down this many numbers (1)(2)

9. Permutations Example 2: Standing in Line. In how many different ways can Carlos, Sergio, Caleb, DeMoris, Eric, and Brayton stand in line?

10. Permutations Example 2: Standing in Line. In how many different ways can Carlos, Sergio, Caleb, DeMoris, Eric, and Brayton stand in line? P(6,6) = 6 x 5 x 4 x 3 x 2 x 1 = 720 different ways There are 6 people to choose from We are selecting this many people (1)(2)(3)(4)(5)(6)

11. Permutations Example 3: Video Games. If I choose three video games to play at Celebration Station out of ten, in how many different orders can I play those three games?

12. Permutations Example 3: Video Games. If I choose three video games to play at Celebration Station out of ten, in how many different orders can I play those three games? P(10,3) = 10 x 9 x 8 = 720 different orders We are selecting 3 games to play (1)(2)(3) There are 10 games to choose from

13. Permutations Example 4: Arrange letters in a word. In how many different ways can you arrange the letters in the word rainbow?

14. Permutations Example 4: Arrange letters in a word. In how many different ways can you arrange the letters in the word rainbow? P(7,7) = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 ways We are selecting all 7 letters (1)(2)(3) There are 7 different letters to arrange (4)(5)(6)(7)

15. Permutations Guided Practice: Find the value. (1) P(8,3) = ? (2) How many ways can the three members of the debating team be arranged on the stage?

16. Permutations Guided Practice: Find the value. (1) P(8,3) = 8 x 7 x 6 = 336 (2) How many ways can the three members of the debating team be arranged on the stage? P(3,3) = 3 x 2 x 1 = 6 ways P(3,3) = 3 x 2 x 1 = 6 ways

17. Permutations Independent Practice: Find the value. (1) P(6,4) = ? (2) How many ways can 4 books be arranged on a bookshelf?

18. Permutations Independent Practice: Find the value. (1) P(6,4) = 6 x 5 x 4 x 3 = 360 (2) How many ways can 4 books be arranged on a bookshelf? P(4,4) = 4 x 3 x 2 x 1 = 24 ways P(4,4) = 4 x 3 x 2 x 1 = 24 ways

19. Permutations Real World Example: Ice Cream. Joselson Ice Cream store has a total of 31 different flavors. They are running a special where you can get three scoops for the price of one. How many ways can you order three different flavored scoops.

20. Permutations Real World Example: Ice Cream. Joselson Ice Cream store has a total of 31 different flavors. They are running a special where you can get three scoops for the price of one. How many ways can you order three different flavored scoops. P(31,3) = 31 x 30 x 29 = 26,970 different ways Start with this number Count down this many numbers (1)(2)(3)

21. Permutations Summary: - Permutations involve arrangements or listings where order is important. - We use the following notation: P(9,4) = * The symbol P(9,4) represents the number of permutations of 9 possible things to take, and we are taking 4 of them

22. Permutations Summary: - Permutations involve arrangements or listings where order is important. - We use the following notation: P(9,4) = 9 x 8 x 7 x 6 = Start with this number Count down this many numbers Permutation

23. What is Factorial? The Factorial of a specified number refers to the product of a given series of consecutive whole numbers beginning with 1 and ending with the specified number The Factorial of a specified number refers to the product of a given series of consecutive whole numbers beginning with 1 and ending with the specified number We use the “!” to represent factorial We use the “!” to represent factorialEg. 5! = 1  2  3  4  5 = 120 Factorial (not in the range)

24. It’s A Fact! The number of ways of arranging n objects is n! n! = n  (n − 1)  (n − 2) ...  3  2  1

25. Calculators 6 x! n! = 720 9 x!  8 = 9

26. Using Permutations Factorial Formula for Permutations

27. Using Permutations How many ways can you select two letters followed by three digits for an ID if repeats are not allowed? Two parts: 2. Determine the set of three digits.1. Determine the set of two letters. 26 P 210 P 3 26  25 650 10  9  8 720 650  720 468,000

28. Homework: Pages 127-128 Permutations