Counting & Probability

The addition, multiplication, and complement rules that everything else builds on.

Ordered arrangements versus unordered selections, and the formulas for each.

Counting integer solutions to distribution problems.

Counting unions of overlapping sets without double-counting.

Proving something must happen just by counting containers and items.

Classical probability, conditional probability, and independence.

Indicator variables and linearity of expectation for problems that resist direct counting.

Block and gaps methods for adjacency and spacing constraints.

Anagram counting with repeated letters and adjacency restrictions.

Lattice-path counting, with obstacles and diagonal moves.

Choosing between complement counting, casework, and inclusion-exclusion.