Permutations & Combinations for discreate mathemeatics

1. Permutations &
Combinations

2. Introduction
• Permutations and combinations are methods to count
possible arrangements of items.

3. What is a Permutation?
• A permutation is an arrangement of objects in a specific
order. Formula: P(n, r) = n! / (n-r)!

4. What is a Combination?
• A combination is a selection of objects without considering
the order. Formula: C(n, r) = n! / (r!(n-r)!)

8. Permutation Question 1
• If there are 3 books and you need to arrange 3 of them on a
shelf, how many ways can you do this?

9. Answer to Question 1
• Using the formula P(n, r) = n! / (n-r)!
• P(3, 3) = 3! / (0)!
• Solution: 6

10. Permutation Question 2
• If there are 4 books and you need to arrange 4 of them on a
shelf, how many ways can you do this?

11. Answer to Question 2
• Using the formula P(n, r) = n! / (n-r)!
• P(4, 4) = 4! / (0)!
• Solution: 24

12. Permutation Question 3
• If there are 5 books and you need to arrange 2 of them on a
shelf, how many ways can you do this?

13. Answer to Question 3
• Using the formula P(n, r) = n! / (n-r)!
• P(5, 2) = 5! / (3)!
• Solution: 20

14. Permutation Question 4
• If there are 6 books and you need to arrange 3 of them on a
shelf, how many ways can you do this?

15. Answer to Question 4
• Using the formula P(n, r) = n! / (n-r)!
• P(6, 3) = 6! / (3)!
• Solution: 120

16. Permutation Question 5
• If there are 7 books and you need to arrange 4 of them on a
shelf, how many ways can you do this?

17. Answer to Question 5
• Using the formula P(n, r) = n! / (n-r)!
• P(7, 4) = 7! / (3)!
• Solution: 840

18. Permutation Question 6
• If there are 8 books and you need to arrange 2 of them on a
shelf, how many ways can you do this?

19. Answer to Question 6
• Using the formula P(n, r) = n! / (n-r)!
• P(8, 2) = 8! / (6)!
• Solution: 56

20. Permutation Question 7
• If there are 9 books and you need to arrange 3 of them on a
shelf, how many ways can you do this?

21. Answer to Question 7
• Using the formula P(n, r) = n! / (n-r)!
• P(9, 3) = 9! / (6)!
• Solution: 504

22. Permutation Question 8
• If there are 10 books and you need to arrange 4 of them on
a shelf, how many ways can you do this?

23. Answer to Question 8
• Using the formula P(n, r) = n! / (n-r)!
• P(10, 4) = 10! / (6)!
• Solution: 5040

24. Permutation Question 9
• If there are 11 books and you need to arrange 2 of them on
a shelf, how many ways can you do this?

25. Answer to Question 9
• Using the formula P(n, r) = n! / (n-r)!
• P(11, 2) = 11! / (9)!
• Solution: 110

26. Permutation Question 10
• If there are 12 books and you need to arrange 3 of them on
a shelf, how many ways can you do this?

27. Answer to Question 10
• Using the formula P(n, r) = n! / (n-r)!
• P(12, 3) = 12! / (9)!
• Solution: 1320

28. Combination Question 1
• If there are 6 students in a class and you need to select a
team of 3, how many ways can you do this?

29. Answer to Combination Question 1
• Using the formula: C(n, r) = n! / (r!(n-r)!)
• C(6, 3) = 6! / (3! * (3)!)
• Solution: 20

30. Combination Question 2
• If there are 7 students in a class and you need to select a
team of 4, how many ways can you do this?

31. Answer to Combination Question 2
• Using the formula: C(n, r) = n! / (r!(n-r)!)
• C(7, 4) = 7! / (4! * (3)!)
• Solution: 35

32. Combination Question 3
• If there are 8 students in a class and you need to select a
team of 5, how many ways can you do this?

33. Answer to Combination Question 3
• Using the formula: C(n, r) = n! / (r!(n-r)!)
• C(8, 5) = 8! / (5! * (3)!)
• Solution: 56

34. Combination Question 4
• If there are 9 students in a class and you need to select a
team of 2, how many ways can you do this?

35. Answer to Combination Question 4
• Using the formula: C(n, r) = n! / (r!(n-r)!)
• C(9, 2) = 9! / (2! * (7)!)
• Solution: 36

36. Combination Question 5
• If there are 10 students in a class and you need to select a
team of 3, how many ways can you do this?

37. Answer to Combination Question 5
• Using the formula: C(n, r) = n! / (r!(n-r)!)
• C(10, 3) = 10! / (3! * (7)!)
• Solution: 120

38. Combination Question 6
• If there are 11 students in a class and you need to select a
team of 4, how many ways can you do this?

39. Answer to Combination Question 6
• Using the formula: C(n, r) = n! / (r!(n-r)!)
• C(11, 4) = 11! / (4! * (7)!)
• Solution: 330

40. Combination Question 7
• If there are 12 students in a class and you need to select a
team of 5, how many ways can you do this?

41. Answer to Combination Question 7
• Using the formula: C(n, r) = n! / (r!(n-r)!)
• C(12, 5) = 12! / (5! * (7)!)
• Solution: 792

42. Combination Question 8
• If there are 13 students in a class and you need to select a
team of 2, how many ways can you do this?

43. Answer to Combination Question 8
• Using the formula: C(n, r) = n! / (r!(n-r)!)
• C(13, 2) = 13! / (2! * (11)!)
• Solution: 78

44. Combination Question 9
• If there are 14 students in a class and you need to select a
team of 3, how many ways can you do this?

45. Answer to Combination Question 9
• Using the formula: C(n, r) = n! / (r!(n-r)!)
• C(14, 3) = 14! / (3! * (11)!)
• Solution: 364

46. Combination Question 10
• If there are 15 students in a class and you need to select a
team of 4, how many ways can you do this?

47. Answer to Combination Question 10
• Using the formula: C(n, r) = n! / (r!(n-r)!)
• C(15, 4) = 15! / (4! * (11)!)
• Solution: 1365

48. Thank You!
Hope you enjoyed learning about permutations and
combinations!