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Contents
1. What is Combinatorics? 2. The Pigeonhole Principle ¡×2.1 The simple form of pigeonhole principle ¡×2.2 The strong form of pigeonhole principle 3. Permutations and Combinations ¡×3.1 Basic Counting Principles: Addition and Multiplication Principles ¡×3.2 Permutations Of sets ¡×3.3 Combinations Of sets ¡×3.4 Permutations Of Multi-sets ¡×2.5 Combinations Of Multi-sets ¡×2.6 Inversions In Permutations 4. The Binomial Coe?cients ¡×4.1 Pascal¡¯s Formula ¡×4.2 The Binomial Theorem ¡×4.3 Binomial Identities ¡×4.4 The Multinomial Theorem 5. The Inclusion-Exclusion Principle ¡×5.1 The Inclusion-Exclusion Principle ¡×5.2 Combinations With Repetition

2

6. Recurrence Relations ¡×6.1 The Fibonacci Sequence ¡×6.2 Iteration and Induction ¡×6.3 Homogeneous Recurrence relations ¡×6.4 Nonhomogeneous Recurrence relations 7. Generating Functions ¡×7.1 Generating Functions ¡×7.2 Partitions of Integers ¡×7.3 Exponential Generating Fun


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