COMB

Counting and combinatorics

The counting machinery behind every probability question: four standard cases, two techniques, and the arguments that prove something cannot be done.

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  1. 1

    Basic counting

    Permutations, combinations, stars and bars, and telling the four cases apart.

  2. 2

    Binomial coefficients

    Pascal, hockey-stick, Vandermonde and the double-counting technique.

  3. 3

    Inclusion–exclusion and invariants

    Derangements, the hat-check problem, pigeonhole and parity arguments.

  4. 4

    Advanced structures

    Catalan numbers, the ballot problem, lattice paths and the reflection principle.