Mathematics of Choice: Or, How to Count Without Counting |
Contents
Chapter 1 Introductory Questions | 1 |
Chapter 2 Permutations and Combinations | 7 |
Chapter 3 Combinations and Binomial Coefficients | 27 |
Chapter 4 Some Special Distributions | 50 |
Chapter 5 The InclusionExclusion Principle Probability | 67 |
Chapter 6 Partitions of an Integer | 91 |
Chapter 7 Generating Polynomials | 100 |
Chapter 8 Distribution of Objects Not All Alike | 109 |
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Common terms and phrases
adjacent alike arrangements batches binomial binomial expansion blocks blue faces c₁ cents chapter chromatic triangle circular permutations coefficient coins colors consider corresponds denote the number derangements distinct objects Evaluate example expansion factors Fibonacci Find the number five formula 3.2 four Hence the answer inclusion-exclusion principle inclusive integers satisfying interpretations least letters mathematical induction minus signs multiplication principle natural numbers non-negative integers number of distributions number of equally number of favorable number of objects number of partitions number of permutations number of regions number of solutions P₁ pairs Pascal's formula Pascal's triangle pigeonhole principle plane points positive integers preceding problem preceding question probability Problem Set property ẞ Prove selected sigma notation solutions in positive solutions of equation solutions of x1 subsets symbols telescoping sum things tions total number write x₁ zero