The sixteenth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers cardinality of finite sets: n-sets and k-subsets of sets. Discussion of injections, surjections and bijections between finite sets, including the Pigeonhole Principle. Contrast with infinite sets. Cardinalities of unions of sets: the Inclusion-Exclusion Principle (see Workshop 8 for more details). Binomial coefficients and the Binomial Theorem.