Contents

Preface

Notation and Abbreviation

1.   The Addition Principle

Exercise

2.   The Multiplication Principle

Exercise

3.   Subsets and Arrangements

Exercise

4.   Applications

Exercise

5.   The Bijection Principle

Exercise

6.   Distribution of Balls into Boxes

Exercise

7.   More Applications of (BP)

Exercise

8.   Distribution of Distinct Objects into Distinct Boxes

Exercise

9.   Other Variations of the Distribution Problem

Exercise

10. The Binomial Expansion

Exercise

11. Some Useful Identities

Exercise

12. Pascal’s Triangle

Exercise

13. The Principle of Inclusion and Exclusion

Exercise

14. General Statement of the Principle of Inclusion and Exclusion

Exercise

15. The Pigeonhole Principle

Exercise

16. Recurrence Relations

Exercise

17. The Stirling Numbers of the First Kind

Exercise

18. The Stirling Numbers of the Second Kind

Exercise

19. The Catalan Numbers

Exercise

20. Miscellaneous Problems

Books Recommended for Further Reading

Answers to Exercises

Index