PERMUTATIONS and COMBINATIONS

1. CHAPTER 7 PERMUTATIONSandCOMBINATIONS 7.1 – Permutations 7.2 – Combinatons 1

2. 9.1 – Permutations OBJECTIVES a) Understand the techniques of counting. b) Understand permutations of a set of objects with some conditions. 2

3. Permutation of a set of objects 3

4. 4

5. Multiplication Principle 5

6. TAXI FLIGHT BUS VAN FERRY TRAIN Let’s consider this question… JOHOR PENANG LANGKAWI 6

7. Example 1 A shop stocks T-shirts in three sizes : small, medium and large. They are available in four colours; black , red , yellow and green. If the sizes are denoted by S, M and L and the colours are denoted by B, R, Y and Gmake a list of all the different labels needed to distinguish the T-shirts and find the number of different labels. 7

8. Solution 1

9. n factorial, n! 9

10. Permutation of n different objects 10

11. 11

12. Example 2 Solution 2 12

13. Example 3 Solution 3

14. Example 4 14

15. Solution 4

16. 16

17. 4 3 17

18. Example 5 18

19. Solution 5

20. Example 6 20

21. Solution 6

22. Permutation with conditions Example 7 22

23. Solution 7

24. Example 8 24

25. Solution 8

26. Example 9 26

27. Solution 9(a)

28. Solution 9(b) 28

29. Example 10 29

30. Solution 10

31. Example 11 31

32. Solution 11

33. Solution 11

34. Example 12 34

35. Solution 12

36. Solution 12 36

37. Permutation where some objects are REPEATED D E F E A T E D Identical objects 37

39. Example 13 Solution 13 39

40. Example 14 Solution 14 40

41. Example 15 41

42. Solution 15

43. Solution 15 43

44. Solution 15 44

45. Solution 15 45

46. Exercise 1 Ans = 120 ways Exercise 2 720 ways 480 ways 46

47. Exercise 3 Ans = 2880 ways Exercise 4 420 ways 1024 ways 48

48. 7.2 – Combinations OBJECTIVES • Understand the combinations of a set of objects. • b)Determine the number of ways to form combination of r objects from n objects.

49. Combinations