This book is the essential companion to the authors’ earlier book Counting (World Scientific, 2002), an introduction to combinatorics for junior college students. It provides supplementary material both for the purpose of adding to the reader’s knowledge about counting techniques and, in particular, for use as a textbook for junior college students and teachers in combinatorics at H3 level in the new Singapore mathematics curriculum for junior college. The emphasis in combinatorics within the syllabus is to hone basic skills and techniques in general problem solving and logical thinking. The book also gives solutions to the exercises in Counting. There is often more than one method to solve a particular problem and the authors have included alternative solutions whenever they are of interest.

Contents:

• Supplementary Chapters:
• The Principle of Inclusion and Exclusion
• General Statement of the Principle of Inclusion and Exclusion
• The Pigeonhole Principle
• Recurrence Relations — An Introduction
• The Stirling Numbers of the First Kind
• The Stirling Numbers of the Second Kind
• The Catalan Numbers
• Solutions to Problems:
• The Addition Principle
• The Multiplication Principle
• Subsets and Arrangements
• Applications
• The Bijection Principle
• Distribution of Balls into Boxes
• More Applications of (BP)
• Distribution of Distinct Objects into Distinct Boxes
• Other Variations of the Distribution Problem
• The Binomial Expansion
• Some Useful Identities
• Pascal’s Triangle
• Solutions to Miscellaneous Problems