Combinatorics

  1. The Binomial Theorem
    1. Pascal's Triangle
      1. Construction and Properties
        1. Patterns in Pascal's Triangle
          1. Combinatorial Identities
            1. Symmetry Properties
              1. Row and Diagonal Sums
              2. The Binomial Expansion
                1. Statement of the Binomial Theorem
                  1. Coefficient Interpretation
                    1. Examples of Expansions
                      1. Negative and Fractional Exponents
                      2. Binomial Identities
                        1. Vandermonde's Identity
                          1. Hockey Stick Identity
                            1. Chu-Vandermonde Identity
                              1. Sum of Binomial Coefficients
                                1. Alternating Sum Identity
                                2. The Multinomial Theorem
                                  1. Statement and Formula
                                    1. Multinomial Coefficients
                                      1. Relationship to Binomial Theorem
                                        1. Applications and Examples

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                                      4. Combinations

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                                      6. Advanced Counting Techniques