Combinatorics, permutations, combinations, selections, pigeonhole principle, inclusion-exclusion.

Basics of counting, pigeonhole principle, permutations and combinations, binomial coefficients and identities, generalized permutations and combinations

Textbook 50 pages

Introduction to combinatorics, choosing elements from a set, permutations, samples.

Lecture notes

Combinations, selections pigeonhole principle, another view of inclusion-exclusion.

Generalized combinations, distinguishable vs. indistinguishable objects, generation of permutations and combinations.

Screencast on counting basics (Trevor)

Screencast 12 minutes TrevTutor

Screencast on factorials and permutations (Trevor)

Screencast 17 minutes TrevTutor

Screencast on solving permutation problems (Trevor)

Screencast 15 minutes TrevTutor

Screencast on combinations (Trevor)

Screencast 18 minutes TrevTutor

Screencast on the binomial theorem (Trevor)

Screencast 16 minutes TrevTutor

Screencast on solving counting problems (Trevor)

Screencast 13 minutes TrevTutor

Screencast on the pigeonhole principle (Trevor)

Basic counting problems (how many ways…) (Rosen Section 6.1)

Problems

Solutions

Apply the pigeonhole principle (Rosen Section 6.2)

Listing permutations and combinations (Rosen Section 6.3)

Find coefficients (Rosen Section 6.4)

Combinations and permutations (continued) (Rosen Section 6.5)