1. PERMUTATION & COMBINATION

3. Multiplication Rule/Principle Adidas Reebox Nike 10 23 7 9 2 3 4   24 = The number of ways the outfit can be chosen =

8. Tom & Jerry Jerry & Tom How many arrangements? 2 PERMUTATIONS

9. Tom & Jerry Jerry & Tom They are the same cat & the mouse OR How many combinations? 1 COMBINATION

10. DIFFERENCES BETWEEN PERMUTATIONS AND COMBINATIONS PERMUTATIONS COMBINATIONS Arranging people, digits, numbers, alphabets, letters, colours. Keywords: Arrangements, arrange,… Selection of menu, food, clothes, subjects, teams. Keywords: Select, choice,…

12. Number of ways to arrange 3 different objects A B C A B C B B A C C A C A B C B A 6 ways A B C

13. Number of ways to arrange 4 different objects A B C D B C D 24 A B C D A B C D A B C D A B C D A B C D A B C D

14. Number Number of of objects ways 1 ……… ……………………… 2 ………. …….………………… 3 ……….. ……………….……… 4 ……….. ……………….……… 1 2 x 1 1 2 6 3 x 2 2 x 1 24 4 x 6 3 x 2 x 1 120 5 x 24 4 x 3 x 2 x 1 6 x 5 x 4 x 3 x 2 x 1 = 6! = 5! = 4! = 3! = 2! = 1! The number of ways to arrange n objects = n ! 5 ……….. ………………………. 6 ……….. ………………………. Factorial

15. 1. To arrange 10 different objects = 10 ! 2. To arrange digits 2, 5, 6, 8 = 4 ! 4 different objects 3. To arrange 12 finalists 12 different objects = 12 !

16. DNA 23 pairs of chromosomes 23 ! different ways to arrange

17. The number of ways to arrange 23 different objects ? 25852016738884976640000 23 ! = 2.6 x 10 22

19. 8 choices 7 choices 6 choices 5 choices 4 choices Number of ways to arrange 5 students from 8 students. 8 x 7 x 6 x 5 x 4 = 6720

20. 8 choices 7 choices 6 choices 5 choices 4 choices number of ways to arrange r from n objects n (n-1) (n-2) (n-3) (n-(r-1))

22. Condition 1 Find the number of ways to form 5 letter word from the letters W, O,R, L, D, C, U, P with the condition that it must starts with a vowels. is filled first W R L D C P O O U 2 7 6 5 4 U =1680

23. Find the number of ways to form 6 letter word from the letters B, E, C, K, H, A, M with the condition that it must starts with a consonant. B CKHM 5 EA 6 5 5x6x5x4x3x2 = 1200 4 3 2

25. A E A E P N L T Y P N L T Y A E 6 ! 2! = 1440 4. To arrange PENALTY such that vowels are side by side 1 2 3 4 5 6 

28. Combinations n objects choose n = 1

29. N = 4 Choose 1: A B C D A B C D Choose 2: A B A C A D B C Choose 3: A B C A C D B C D B D C D A B D Choose 4: A B C D = 4 = 4 C 1 = 6 = 4 C 2 = 4 = 4 C 3 = 1 = 4 C 4

30. Combinations

32. Conditional Combination 1 A football team has 17 local players and 3 imported players. Eleven main players are to be chosen with the condition that it must consist of 2 imported players. Find the number of ways the main player can be chosen. import local 3 17 2 9 3 C 2 17 C 9   = 72930 r n

33. Condition Combination 2 A committee consisting of 6 members is to be chosen from 3 men and 4 women. Find the number of ways at least 3 women are chosen. W3 M3 , or W4 M2 , 4 C 3 X 3 C 3 + 4 C 4 X 3 C 2 = 7

38. Find the number of ways to form 6 letter word from the letters B, E, C, K, H, A, M with the condition that it must starts with a consonant. B CKHM 5 EA 6 5 5x6x5x4x3x2 = 1200 4 3 2

40. PROBABILITY