In this talk, I will give an overview of some tools used in probabilistic combinatorics, and illustrate their use in two different projects. First, in joint work with Marcus Michelen and Will Perkins, we establish an asymptotic formula for the number of integer partitions of a general type: namely, partitions of an integer n where the sums of the kth powers of the parts are also fixed, for some collection of values k. Second, in joint work with Lina Li and Jinyoung Park, we give enumerative and structural results for colorings of the middle layers of the Hamming cube. This talk does not assume a lot of background, and it’s definitely okay if you don’t know much probability or combinatorics!