Combinatorics is the mathematics of counting, arrangement, and combination of objects — fundamental to algorithm analysis, probability, cryptography, and machine learning. This quiz covers permutations, combinations, binomial coefficients, recurrence relations, generating functions, graph theory, and combinatorial designs.

Fundamental Counting Principles

The Product Rule and Sum Rule form the foundation for counting in algorithm analysis and combinatorial problem-solving.

Permutations & Combinations

Permutations count arrangements where order matters: P(n,r) = n!/(n-r)!. Combinations count selections: C(n,r) = n!/(r!(n-r)!). Essential for probability and optimization.

Advanced Techniques

Pigeonhole principle, inclusion-exclusion, stars and bars, recurrence relations, generating functions, and Catalan numbers appear throughout advanced CS problems.