Front Cover -- Mathematics of Choice or How to Count Without Counting -- Copyright Page -- Contents -- Preface -- Chapter 1. Introductory Questions -- Chapter 2. Permutations and Combinations -- 2.1 The Multiplication Principle -- 2.2 Factorials -- 2.3 Permutations -- 2.4 Zero Factorial -- 2.5 Combinations -- 2.6 Permutations of Things in a Circle -- 2.7 Summary -- Chapter 3. Combinations and Binomial Coefficients -- 3.1 A Path Problem -- 3.2 Permutations of Things Not All Alike -- 3.3 Pascal's Formula for C(n, r) -- 3.4 The Binomial Expansion -- 3.5 The Multinomial Expansion -- 3.6 Pascal's Triangle -- 3.7 The Number of Subsets of a Set -- 3.8 Sums of Powers of Natural Numbers -- 3.9 Summary -- Chapter 4. Some Special Distributions -- 4.1 Fibonacci Numbers -- 4.2 Linear Equations with Unit Coefficients -- 4.3 Combinations with Repetitions -- 4.4 Equations with Restricted Solutions -- 4.5 Summary -- Chapter 5. The Inclusion-Exclusion Principle -- Probability -- 5.1 A General Result -- 5.2 Applications to Equations and to Combinations with Repetitions -- 5.3 Derangements -- 5.4 Combinatorial Probability -- 5.5 Summary -- Chapter 6. Partitions of an Integer -- 6.1 Graphs of Partitions -- 6.2 The Number of Partitions -- 6.3 Summary -- Chapter 7. Generating Polynomials -- 7.1 Partitions and Products of Polynomials -- 7.2 Change for a Dollar Bill -- 7.3 Summary -- Chapter 8. Distribution of Objects Not All Alike -- 8.1 Objects Different, Boxes Different -- 8.2 Objects Different, Boxes Alike (Partitions of a Set) -- 8.3 Objects Mixed, Boxes Different -- 8.4 Summary -- Chapter 9. Configuration Problems -- 9.1 The Pigeonhole Principle -- 9.2 Chromatic Triangles -- 9.3 Separations of the Plane -- 9.4 Summary -- Chapter 10. Mathematical Induction -- 10.1 The Principle of Mathematical Induction -- 10.2 Notation for Sums and Products -- 10.3 Summary.

Chapter 11. Interpretations of a Non-Associative Product -- 11.1 A Recursion Relation -- 11.2 The Development of an Explicit Formula -- 11.3 Proof of the Conjecture -- 11.4 A Formula for F(n) -- 11.5 Summary -- Miscellaneous Problems -- Answers and Solutions -- Bibliography -- Index.