Combinatorics has played an important role in the development of reverse mathematics, with a particular focus on Ramsey's theorem. This tutorial will be an attempt to survey some of the central themes in this investigation, but with a modern twist. Namely, it will be centered around recent work by Benham, DeLapo, Dzhafarov, Solomon, and Villano exploring the proof-theoretic and computability-theoretic strength of the Ginsburg--Sands theorem, a result in topology with a surprising connection to Ramsey's theorem for pairs. We will thus have an opportunity also to see a formalization of some basic notions from point-set topology and how this facilitates both the study of the Ginsburg--Sands theorem as well as its link to combinatorics. The tutorial will include a review of some basic concepts in reverse mathematics, focusing on the interval between ACA_0 and RCA_0.