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Mathematics
Combinatorics
1. Introduction to Combinatorics
2. Fundamental Counting Principles
3. Permutations
4. Combinations
5. The Binomial Theorem
6. Advanced Counting Techniques
7. Recurrence Relations
8. Generating Functions
9. Special Counting Numbers and Sequences
10. Graph Theory and Combinatorics
11. Design Theory
12. Probabilistic Combinatorics
13. Algebraic Combinatorics
14. Extremal Combinatorics
15. Applications and Advanced Topics
4.
Combinations
4.1.
Selections of Distinct Objects
4.1.1.
Definition of Combination
4.1.2.
The Binomial Coefficient C(n,k)
4.1.3.
Properties of Binomial Coefficients
4.1.4.
Symmetry Property
4.1.5.
Pascal's Rule
4.1.6.
Relationship to Permutations
4.2.
Combinations with Repetition
4.2.1.
Definition and Examples
4.2.2.
Multisets
4.2.3.
The Stars and Bars Method
4.2.3.1.
Basic Principle
4.2.3.2.
Derivation of Formula
4.2.3.3.
Worked Examples
4.2.3.4.
Variations and Extensions
4.2.4.
Formula for Combinations with Repetition
4.2.5.
Applications to Distribution Problems
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3. Permutations
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5. The Binomial Theorem