Peter Shor continues MIT's 18.200, Principles of Discrete Applied Mathematics, with a lecture on combinatorial counting techniques. He proves Cayley's tree theorem, which counts the number of labeled trees on n vertices, by counting the same set two different ways, a classic double-counting argument. The lecture then turns to generating functions, introducing what they are and how to combine them through addition and multiplication to encode combinatorial sequences. Shor works through the definitions and operations on the board, building toward how generating functions become tools for solving counting problems later in the course. The seventy-two minute session is aimed at students already familiar with basic combinatorics from earlier lectures in the sequence.