Comprehensive chapter review of counting techniques including Pascal’s triangle, sum/product principles, permutations, combinations, stars and bars, PIE, and combinatorial proofs. Contains extensive practice problems integrating all counting methods with solutions strategies.
Advanced counting problems using Principle of Inclusion-Exclusion for multiple sets. Covers derangements (permutations with no fixed points), counting surjective functions, distributing distinguishable objects, and solving complex overlap problems.
Explores combinatorial proof techniques using bijections and double counting. Shows how to prove binomial identities by counting the same set in two different ways. Includes Pascal’s identity, subset selection proofs, and bijective correspondences.
Introduces stars and bars technique for distributing indistinguishable objects into distinguishable bins. Covers applications to integer solutions of equations, cookie distribution problems, and variations with restrictions on minimum or maximum quantities.
Detailed treatment of permutations (ordered selections) versus combinations (unordered selections). Includes formulas for P(n,k) and C(n,k), applications to word arrangements, committee selections, and problems with restrictions or repetition allowed.