SMO Senior · 11. Counting, probability and combinatorics
Count with structure, turn counts into probabilities, force existence with pigeonholes, and control processes with invariants.
Choose between the multiplication rule, cases, stars and bars, the gap method and inclusion–exclusion.
Compute classical, conditional and binomial probabilities from equally likely cases.
Solve "smallest N" problems with a pigeonhole bound and a matching construction.
Find and prove an invariant for an operation or game problem.
Check every counting answer by a second method or a small case.