Combinatorics & Counting

Read these first

1. 01Permutations and Combinations

   The two questions that count everything: does order matter, and are repeats allowed. Get the answer right and a seating chart, a poker hand, and a binomial tree all reduce to the same arithmetic.

2. 02Generating Functions in Combinatorics

   A trick for turning a counting problem into an algebra problem: encode a whole sequence of numbers as the coefficients of one polynomial, then multiply polynomials instead of reasoning about cases by hand.

Then the rest

1. 03Binomial Coefficients and Pascal's Triangle
2. 04The Pigeonhole Principle
3. 05Balls and Bins and the Birthday Problem
4. 06Catalan Numbers
5. 07Graph Theory Basics
6. 08Recurrence Relations
7. 09The Inclusion-Exclusion Principle
8. 10The Probabilistic Method