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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.
The Addition Principle
The Multiplication Principle
Subsets and Arrangements
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
The Principle of Inclusion and Exclusion
General Statement of the Principle of Inclusion and Exclusion
The Pigeonhole Principle
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.
Rigorous and clear solutions
Introductory section on problem solving as described by Georg Polya