ILLUSTRATING AND DIFFERENTIATING COMBINATION AND PERMUTATION.pptx

COMBINATION AND PERMUTATION

1. Illustrating and Differentiating Permutation from Combination of n Objects taken r at a Time Quarter 3- Lesson 6

2. ACTIVITY 1: AM I IMPORTANT OR NOT? Direction: Read the following items carefully. Identify the following situation if order is important or NOT important. In your Math notebook, write AI if order is important and NI if order is NOT important.

3. ACTIVITY 1: AM I IMPORTANT OR NOT? Four people posing for pictures.

4. ACTIVITY 1: AM I IMPORTANT OR NOT? 2. Determining the top three winners in a Math Quiz Bee.

5. ACTIVITY 1: AM I IMPORTANT OR NOT? 3. Choosing 2 household chores to do before dinner.

6. ACTIVITY 1: AM I IMPORTANT OR NOT? 4. Arranging 6 potted plants in a row

7. ACTIVITY 1: AM I IMPORTANT OR NOT? 5. Selecting 5 basketball players out of 10 team members for the different positions.

8. LET’S CHECK YOUR ANSWERS!!!

9. ACTIVITY 1: AM I IMPORTANT OR NOT? Four people posing for pictures. AI (Order is Important)

10. ACTIVITY 1: AM I IMPORTANT OR NOT? 2. Determining the top three winners in a Math Quiz Bee. AI (Order is Important)

11. ACTIVITY 1: AM I IMPORTANT OR NOT? 3. Choosing 2 household chores to do before dinner. NI (Order is NOT Important)

12. ACTIVITY 1: AM I IMPORTANT OR NOT? 4. Arranging 6 potted plants in a row AI (Order is Important)

13. ACTIVITY 1: AM I IMPORTANT OR NOT? 5. Selecting 5 basketball players out of 10 team members for the different positions. AI (Order is Important)

14. Lesson 6: what is combination in math? Combination is an arrangement of objects in which the order is not important . This is different from permutation where the order is important.

15. Lesson 6: what is combination in math? For example, suppose we are arranging the letters A, B, and C. In a permutation , the arrangements ABC and ACB are different. But, in a Combination , the arrangements ABC and ACB are the same because the order is not important.

16. COMBINATION Refers to the selection of an object regardless of their order. It is selection of things in which ORDER/ARRANGEMENT IS NOT IMPORTANT Changing the order of the objects does not create combination

17. COMBINATION The combination of n objects taken r at a time is: C where n ≥ r ≥ 0   n r

18. COMBINATION The combination of n objects taken all at a time is: C   n r

19. EXAMPLES Evaluate: 6 C 4 Ans: 15 combinations

20. EXAMPLES In how many ways can a committee consisting of 4 members be formed from 8 people? Ans: 70 ways Therefore, a committee consisting of 4 members be formed from 8 people in 70 ways.

21. Difference between permutation & combination question Problem 1: From 3 players, A, B, and C, how many double-teams can be formed? COMBINATION The team (A B) is the same as the team (B A) Arrangement of the “team members” does not affect the team composition Problem 2: From 3 letters, A, B, and C, how many 2-digit words can be formed? PERMUTATION The word AB is not the same as the word BA. The arrangement of the letters can give us two different word

22. Difference between permutation & combination question Problem 1: From 3 players, A, B, and C, how many double-teams can be formed? COMBINATION AB or BA  1 AC or CA  1 BC or CB  1 Answer: 3 double-teams Problem 2: From 3 letters, A, B, and C, how many 2-digit words can be formed? PERMUTATION AB, BA  2 AC, CA  2 BC, CB  2 Answer: 6 two-digit words

23. Difference between permutation & combination question COMBINATION Some Keywords: SELECT CHOOSE PICK COMBINATION PERMUTATION Some Keywords: ARRANGE ORDERED WAYS UNIQUE DIFFERENT SEQUENCE

24. Note! If Keywords are not given, then visualize the scenario presented in the question and then think in terms of combination and arrangement.

25. examples 2. Selecting 5 problems in a 10-item Mathematics problem-solving test. - It is a combination because selecting 5 problems in a 10-Item Mathematics problem solving test does not need an order, hence it was not specified if you need to choose it by it’s difficulty.

26. examples Five badminton players chosen from a group of nine. - It is a combination because when choosing a badminton player within a group does not require an order or arrangement.

27. Direction: Determine whether each situation involves a combination or permutation. Write C if it involves combination and P if it involves permutation. 1. Choosing 6 volleyball players from a group of 12. 2. Seven (7) toppings for a pizza. 3. Finding the diagonals of a polygon. 4. Arranging 4 people in a row for picture taking. 5. Assigning 5 different tasks to top 5 students.

28. PRACTICE EXERCISE

29. Direction: Determine whether each situation involves a combination or permutation. Write C if it involves combination and P if it involves permutation. C 1. Choosing 6 volleyball players from a group of 12. C 2. Seven (7) toppings for a pizza. C 3. Finding the diagonals of a polygon. P 4. Arranging 4 people in a row for picture taking. P 5. Assigning 5 different tasks to top 5 students.

30. EVALUATION TEST

31. PART I: Directions : Determine whether each problem involves a combination or permutation. Write your answer in your notebook. 1. In how many ways can you arrange 5 Mathematics books, 4 Science books, and 3 English books on a shelf such that books of the same subject are kept together? 2. If there are 12 teams in a basketball tournament and each team must play every other team in the eliminations. 3. How many 4-digit numbers can be formed from the digits 1, 3, 5, 6, 8, and 9 if no repetition is allowed? 4. In a gathering, the host makes sure that each guest shakes hands with everyone else. If there are 25 guests, how many handshakes will be done? 5. The teacher determines the number of top 10 students in Mathematics class.

32. PART II: Direction: Find the combination. In a 10-item Mathematics problem-solving test, how many ways can you select 5 problems to solve? Show your solution.

33. LET’S CHECK YOUR ANSWER!

34. Directions : Determine whether each problem involves a combination or permutation. Write your answer in your notebook. In how many ways can you arrange 5 Mathematics books, 4 Science books, and 3 English books on a shelf such that books of the same subject are kept together? PERMUTATION 2. If there are 12 teams in a basketball tournament and each team must play every other team in the eliminations. COMBINATION

35. Directions : Determine whether each problem involves a combination or permutation. Write your answer in your notebook. 3. How many 4-digit numbers can be formed from the digits 1, 3, 5, 6, 8, and 9 if no repetition is allowed? PERMUTATION 4. In a gathering, the host makes sure that each guest shakes hands with everyone else. If there are 25 guests, how many handshakes will be done? COMBINATION

36. Directions : Determine whether each problem involves a combination or permutation. Write your answer in your notebook. 5. The teacher determines the number of top 10 students in Mathematics class. PERMUTATION

37. PART II: Direction: Find the combination. In a 10-item Mathematics problem-solving test, how many ways can you select 5 problems to solve? Show your solution. Answer: 252 ways Therefore, there are 252 ways to select 5 problems to solve in a 10-item Mathematics problem solving test.

38. JOB WELL-DONE!