(This list is subject to change and is not the same every year. The topics are not in order.)
Introduction to combinatorics.
Sections 1, 2, 3, 5 on various types of combinatorial problems.
Sections 1-2: The pigeonhole principle.
All sections: basic counting, with and without repetition.
Sections 1-3, 5: Binomial identities, combinatorial proofs, binomial and multinomial theorems.
Section 4: Unimodality and Sperner's theorem.
Sections 1-5: The Principle of Inclusion and Exclusion and a variety of ways to apply it, notably combinations with repetition, derangements, permutations with forbidden positions, circular permutations with forbidden relations.
Section 1: Modular arithmetic.
Section 4 (first half, to page 403): Latin squares.
Extra: Affine planes.