Counting

Solutions Manual

This book is the essential companion to Counting (2nd Edition) (World Scientific, 2013), an introduction to combinatorics for secondary to undergraduate students. The book gives solutions to the exercises in Counting (2nd Edition). There is often more than one method to solve a particular problem and the authors have included alternative solutions whenever they are of interest.

The rigorous and clear solutions will aid the reader in further understanding the concepts and applications in Counting (2nd Edition). An introductory section on problem solving as described by George Pólya will be useful in helping the lay person understand how mathematicians think and solve problems.

Contents:

• 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
• The Principle of Inclusion and Exclusion
• General Statement of the Principle of Inclusion and Exclusion
• The Pigeonhole Principle
• Recurrence Relations
• The Stirling Numbers of the First Kind
• The Stirling Numbers of the Second Kind
• The Catalan Numbers
• Solutions to Miscellaneous Problems

Readership: College students and teachers in combinatorics.
Key Features:

• Rigorous and clear solutions
• Alternative solutions
• Introductory section on problem solving as described by Georg Polya