1. Combinatorics

2. 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

3. 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

4. Other Counting sequences
Fibonacci numbers

5. Recursion vs Induction