UsefulLinks
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
5.
The Binomial Theorem
5.1.
Pascal's Triangle
5.1.1.
Construction and Properties
5.1.2.
Patterns in Pascal's Triangle
5.1.3.
Combinatorial Identities
5.1.4.
Symmetry Properties
5.1.5.
Row and Diagonal Sums
5.2.
The Binomial Expansion
5.2.1.
Statement of the Binomial Theorem
5.2.2.
Coefficient Interpretation
5.2.3.
Examples of Expansions
5.2.4.
Negative and Fractional Exponents
5.3.
Binomial Identities
5.3.1.
Vandermonde's Identity
5.3.2.
Hockey Stick Identity
5.3.3.
Chu-Vandermonde Identity
5.3.4.
Sum of Binomial Coefficients
5.3.5.
Alternating Sum Identity
5.4.
The Multinomial Theorem
5.4.1.
Statement and Formula
5.4.2.
Multinomial Coefficients
5.4.3.
Relationship to Binomial Theorem
5.4.4.
Applications and Examples
Previous
4. Combinations
Go to top
Next
6. Advanced Counting Techniques