1. Lecture 08 Counting Profs. Koike and Yukita
Discrete Systems I
Lecture 08
Counting
Profs. Koike and Yukita

2. 1. Basic counting principles

3. Examples

4. 2. Factorial

5. 3. Binomial coefficients

6. 4. Permutations

7. Example

8. Example(continued)

9. Permutations with Repetitions

10. Example

11. Example(continued)

12. Example

13. 5. Combinations

14. Binomial Theorem

15. 6. The Pigeonhole Principle

16. Generalized Pigeonhole Principle

17. 7. The Inclusion-Exclusion Principle

18. 8. Ordered Partitions

19. Ordered partitions 1

20. Example

21. Unordered partition

22. Problem 1

23. Problem 2

24. Problem 3

25. Problem 4

26. Problem 5

27. Problem 6

28. Problem 7

29. Problem 8

30. Problem 9