Combinatorics

Basic Counting Techniques Product Rule: |A| possibilities from set A and |B| possibilities from set B mean |A| x |B| possibilities to combine an element of A with an element of B. Sum rule: |A| possibilities from set A and |B| possibilities from set B mean |A| + |B| possibilities to choose an element from A or B assuming A and B are “disjoint”. Inclusion-Exclusion Formula: Bijections Permutations: Every element of a set appears exactly once. There are |A|! permutations of a set A. Subsets: Strings

Recurrence Relations Binomial Coefficients How many ways are there to form a k member committee of a set of n people? Paths across a grid: How many ways are to to go from the upper left corner of a grid to the lower right? Coefficients of (a+b)^n Pascal’s triangle

Other Counting sequences Fibonacci numbers

Recursion vs Induction