1 / 23

Permutations

Permutations. Permutations. Objectives : (1) Students will be able to use permutations to find all possible arrangements involving a limited number of choices. Essential Questions : (1) What are permutations and how can we find them?. Permutations. What is a Permutation ?

nash-mclaughlin
Download Presentation

Permutations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Permutations

  2. Permutations Objectives: (1) Students will be able to use permutations to find all possible arrangements involving a limited number of choices. Essential Questions: (1) What are permutations and how can we find them?

  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.

  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

  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 (1) (2) (3) Count down this many numbers

  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 (1) (2) We are using this many numbers so we count down this many numbers

  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 (1) (2) (3) (4) (5) (6) We are selecting this many people

  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= 720different orders There are 10 games to choose from (1) (2) (3) We are selecting 3 games to play

  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 = 5040ways There are 7 different letters to arrange (1) (2) (3) (4) (5) (6) (7) We are selecting all 7 letters

  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

  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

  19. Permutations Real World Example:Ice Cream. Coldstone Creamery 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. Coldstone Creamery 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 (1) (2) (3) Count down this many numbers

  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 Permutation Count down this many numbers

  23. Permutations Homework: - Core 01 → p.___ #___, all - Core 02 → p.___ #___, all - Core 03 → p.___ #___, all

More Related