CIRCULAR PERMUTATION for the grade 10.pptx

it is about circular permutation

1. WELCOME TO OUR MATHEMATICS CLASS!

2. Illustrate permutation of identical objects and circular permutation. Solve problems involving permutation of identical objects and circular permutation. Apply the importance of permutation of identical objects and circular permutations. OBJECTIVES

3. ACTIVITY: Trip to Jerusalem Directions: We need five volunteers from the class and we are going to play the game trip to jerusalem , the student who will win the game, will be given additional points.    

4. Activity: Form a Word Directions: Arrange the jumbled letters to form a word. The definitions are provided for you to easily get the right word. Write your answer to any sheet of paper.

5.  ACRILUCR C_ _ _ _ _ _ _ Having a form of circle or round.  

6.   REMTINAPUTO P_ _ _ _ _ _ _ _ _ _ Arranging objects in to different ways.

7.   ODNUAR A_ _ _ _ _ In a position or direction surrounding, or in a direction along the edge of or from one part to another.

8. CIRCULAR PERMUTATION

9. Circular permutation A number of arrangements of objects around a circle (circular table).

10. Rule #1 The number of permutations of n objects around a circle is defined as (n-1)!

11. Example 1: a. In how many ways can 4 people be arranged to sit around a circular table? (n-1)!=(4-1)!=3! =3x2x1= 6 ways

12. Example 2: In how many ways can 5 people be arranged to sit around a circular table? (n-1)!=(5-1)!= 4! =4x3x2x1 =24 ways

13. Rule #2 When n objects such as keys are arranged in circular object (such as key ring) we use

14. Example 1: In how many ways can you arrange 6 keys on key ring. = = =60 ways

15. Example 2: In how many ways a 5 different gemstones be arranged in bracelet? = = = 12 ways

16. Rule #3 The number of circular permutations of n objects taken r at a time is

17. Example 1: In how many ways can 8 delegates in an international conference taken 5 at a time be arranged around a circular table? 8 P 5 = = = = 1,344 ways

18. Example 2: In how many ways can 10 delegates in an international conference taken 4 at a time be arranged around a circular table? 10 P 4 = = = = = 1,260 ways

19. GROUP ACTIVITY Directions: Find the permutation of the given problem. Each group is given a bondpaper and a marker where you write your answer. You only given 30 seconds to answer and raise your answer in the count of 3.

20. 1. Eight people are to be seated at a round table. In how many arrangements are possible? 3. In how many different ways can four keys be arranged on a key-ring? 2. In how many ways can 10 girls be seated at a circular table? 4. How many ways can seven people be seated at a round table inside the room?

21. 2. What are the formula in getting the circular permutations? What is circular permutation? 3. Cite examples where you can apply the concepts of permutation with identical of objects/ distinguishable permutation?

22. Directions : Read and analyze each item carefully. Write the letter of the correct answer on the blank before the item number.

23. ___1. In how many ways can nine people be seated around a circular table? 362,880 b. 40,320 c. 5,040 d. 720 ___2. In how many ways can 12 people be seated around a circular table ? 39,916,800 b. 3,628,800 c. 479,001,600 d. 362,800

24. ___3. Five different keys are to be placed on a circular key chain. How many different arrangements are there? 4 b. 5 c. 12 d. 24 4. In how many ways can five people be seated around a circular table? 24 b. 40,320 c. 5,040 d. 720 ___5. In how many ways can seven people be seated around a circular table? 362,880 b. 40,320 c. 5,040 d. 720

25. B . PROBLEM SOLVING In how many ways can 6 delegates in an international conference taken 3 at a time be arranged around a circular table? In how many ways can 5 participants in a cheer dance competition taken 3 at a time be arranged around a circular table?

26. Assignment FOLLOW UP: Give scenario in your life where you can apply the concept of circular permutation. ADVANCED: Study about combination.

27. THANK YOU!