Combinatorics

  1. Combinations
    1. Selections of Distinct Objects
      1. Definition of Combination
        1. The Binomial Coefficient C(n,k)
          1. Properties of Binomial Coefficients
            1. Symmetry Property
              1. Pascal's Rule
                1. Relationship to Permutations
                2. Combinations with Repetition
                  1. Definition and Examples
                    1. Multisets
                      1. The Stars and Bars Method
                        1. Basic Principle
                          1. Derivation of Formula
                            1. Worked Examples
                              1. Variations and Extensions
                              2. Formula for Combinations with Repetition
                                1. Applications to Distribution Problems

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                              3. Permutations

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                              5. The Binomial Theorem