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The 58 pages that link to Binomial coefficient, each with the reason it gives.

• Baranyai's theoremRelated: It counts the hyperedges that the theorem distributes among its factors.

• Carlson's theoremRelated: Analytic continuations of binomial expressions can be compared using their integer values and growth.

• Combinatorial principlesRelated: It is the central count underlying many arrangement and selection formulas.

• Lah numberRelated: Choosing the k−1 gaps between lists contributes the factor \(\binom{n-1}{k-1}\).

• Lucas's theoremNarrower topic: The theorem computes these coefficients modulo a prime.

• Partial permutationRelated: Choosing the k-element domain contributes the factor that combines with the falling factorial.

• Twelvefold wayRelated: Choosing which boxes receive one object is a basic special case of distribution.

• Wolstenholme's theoremNarrower topic: The theorem concerns a particular binomial coefficient whose divisibility is unusually strong.