Differentiate Permutation from combination [Autosaved].pptx

for math 10

1. Permutation vs Combination

2. Lesson Objectives Differentiate permutation from combination; and Solve permutation or combination of n taken r at a time.

3. Activity: Watch your Order Determine if the given situation requires order or not. Choose the reaction that corresponds to your answer. Order matters Order does not matter

4. Opening a combination lock. Order matters Order does not matter

5. Opening a combination lock. Order matters

6. Assigning seats in a queue. Order matters Order does not matter

7. Assigning seats in a queue. Order matters

8. Selecting balls from a box. Order matters Order does not matter

9. Selecting balls from a box. Order does not matter

10. Forming triangles from set of points with no three points are collinear. Order matters Order does not matter

11. Forming triangles from set of points with no three points are collinear. Order does not matter

12. Watch your Order Order matters Order matters Order does not matter Order does not matter

13. Watch your Order permutation combination permutation combination

14. Take Note SIMILARITY Permutation and combination are both selections made from a group.

15. Take Note DIFFERENCE In permutation, order matters while in combination, order does not matter.

16. Let’s compare ABCD – Find permutations of 2 and combinations of 2. Permutations of 2: AB CA AC CB AD CD BA DA BC DB BD DC Note: AB is NOT the same as BA. Combinations of 2: AB AC AD BC BD CD Note: AB is the same as BA

17. Permutation vs Combination Example Permutations Choosing a first, second, and third place winners from a Beauty Pageant. Combinations Picking Top 10 finalist in no order in a Beauty Pageant.

18. Permutation vs Combination Formula Permutations   Combinations  

19. Examples of relating to Permutations Ranking people. Sequencing of draws. Locking with a definite sequence. Forming of words with the given letters. Forming of numbers with the given digits.

20. Examples of relating to Combinations Handshaking with other. Numbering in no particular order. Picking multiple objects in one draw. Forming a team from a number of players. Forming of a particular committee from a number of players .

21. Always keep an eye on the keywords used in the question. The keywords can help you get the answer easily. The keywords like – selection, choose, pick, and combination – indicates that it is a combination question. Keywords like – arrangement, ordered, unique – indicates that it is a permutation question. If keywords are not given, then visualize the scenario presented in the question and then think in terms of combination and arrangement. Takeaways

22. 1. From 3 tennis players A, B, and C, how many doubles team can be formed? Identify if the given situation illustrates permutation or combination. Then solve the problem. Combination

23. 1. From 3 tennis players A, B, and C, how many doubles team can be formed?   n = 3 r = 2         = 3

24. 2. From 3 letters, A, B, and C, how many 2 – letter words can be formed? Identify if the given situation illustrates permutation or combination. Then solve the problem. Permutation

25. 2. From 3 letters, A, B, and C, how many 2 – letter words can be formed?   n = 3 r = 2        

26. 3. In how many ways can 5 teachers be assigned to 3 sections of the Grade 10 in a high school? Identify if the given situation illustrates permutation or combination. Then solve the problem. Permutation

27.   n = 5 r = 3         3. In how many ways can 5 teachers be assigned to 3 sections of the Grade 10 in a high school?

28. 4. In a society of 10 members, we have to select a committee of 4 members. As the owner of the society, John is already a member of the committee. In how many ways can the committee be formed? Identify if the given situation illustrates permutation or combination. Then solve the problem. Combination

29. 4. In a society of 10 members, we have to select a committee of 4 members. As the owner of the society, John is already a member of the committee. In how many ways can the committee be formed?   n = 9 r = 3          

30. Activities A. Directions: Analyze carefully each problem. Write “ permu ” if it is an example of permutation and “ combi ” if is combination. ____________ 1. getting 3 shirts from 10 choices for a 3-day retreat. ____________ 2. assigning 3 readers for a recollection for 3 different passages. ____________ 3. choosing 5 basketball players from a bench of 12 players for a jump ball. ____________ 4. grabbing 6 marbles from a box of 30 marbles. ____________ 5. determining the succession of film floats in a film festival.

31. 1.A group of 10 women and 6 men must select a four-person committee. How many committees are possible if it must consist of the following: Two men and two women? B. Analyze and solve each problem carefully and accurately. b) majority of women? c) majority of men?

32. Solution: a) 2 men and 2 women n1 = 10 women n2 = 6 men r1 = 2 women r2 = 2 men      

33. (9b) condition: In selecting four-person committee consisting of majority of women , there are 2 scenarios:

34. (8c) condition: In selecting four-person committee consisting of majority of men , there are also 2 scenarios:

35. 2. One of the highlight activities of Sta. Maria Town Fiesta is the MASS WEDDING held every February 14. In the venue, they put round tables around the dancing fountain for couples and each table can hold 5 couples. Consider one of the tables in the venue which is prepared for the first five couples that will arrive. a) How many ways are there to arrange the first five couples in a round table? b) How many arrangements are there where the couples are seated together? c) How many arrangements are there if wives are seated together? d) How many arrangements are there if husband and wife seat alternately?

36. A box contains 7 red balls, 5 yellow balls, and 3 green balls. In how many ways can we select 3 balls such that: a) They are all red? b) They are all yellow? c) They are all green? d) They are of different colors? e) Exactly 2 are yellow?

37. Solution: red = 7 yellow = 5 green = 3 a) They are all red r = 3 n = 7             Select 3 balls

38. Solution: red = 7 yellow = 5 green = 3 b ) They are all yellow r = 3 n = 5             Select 3 balls

39. Solution: red = 7 yellow = 5 green = 3 c) They are all green r = 3 n = 3             Select 3 balls

40. Solution: red = 7 yellow = 5 green = 3 d ) They are of different colors Select 3 balls      

41. Solution: red = 7 yellow = 5 green = 3 e) exactly 2 are yellow r = 3 is distributed             Select 3 balls      

42. Solution: red = 7 yellow = 5 green = 3 e) exactly 2 are yellow r = 3 is distributed             Select 3 balls        

43. Activity: Perfect Combination Study the following situations. Identify which situation involves permutation and which involves combination. Determining the top three winners in a Science Quiz Bee. Forming lines from six given points with no three of which are collinear. Forming triangles from 7 given points with no three of which are collinear. Four people posing for pictures. Assembling a jigsaw puzzle. Choosing 2 household chores to do before dinner. Selecting 5 basketball players out of 10 team members for the different positions. Choosing three of your classmates to attend your party. Picking 6 balls from a basket of 12 balls. Forming a committee of 5 members from 20 people.