Table of Contents
Preface v
Notation and Abbreviation ix
Pólya's Model of Problem Solving 1
1 The Addition Principle 7
2 The Multiplication Principle 15
3 Subsets and Arrangements 23
4 Applications 29
5 The Bijection Principle 41
6 Distribution of Balls into Boxes 51
7 More Applications of (BP) 55
8 Distribution of Distinct Objects into Distinct Boxes 65
9 Other Variations of the Distribution Problem 69
10 The Binomial Expansion 75
11 Some Useful Identities 81
12 Pascal's Triangle 85
13 The Principle of Inclusion and Exclusion 91
14 General Statement of the Principle of Inclusion and Exclusion 97
15 The Pigeonhole Principle 107
16 Recurrence Relations 115
17 The Stirling Numbers of the First Kind 123
18 The Stirling Numbers of the Second Kind 129
19 The Catalan Numbers 133
20 Solutions to Miscellaneous Problems 141
Recommended Books for Further Reading 213
