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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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Probability estimates for "beans & boxes"
I'll agree with the other answers that it's easiest to approximate the bins as independent, but since the problem is discrete, it seems more natural to describe the number of beans in a bin by a binom …