Binomial[n, m] gives the binomial coefficient ( { {n}, {m} } ).

BinomialDistribution[n, p] represents a binomial distribution with n trials and success probability p.

BetaBinomialDistribution[\[Alpha], \[Beta], n] represents a beta binomial mixture distribution with beta distribution parameters \[Alpha] and \[Beta], and n binomial trials.

NegativeBinomialDistribution[n, p] represents a negative binomial distribution with parameters n and p.

BetaNegativeBinomialDistribution[\[Alpha], \[Beta], n] represents a beta negative binomial mixture distribution with beta distribution parameters \[Alpha] and \[Beta], and n ...

QBinomial[n, m, q] gives the q-binomial coefficient (n; m)_q.

MultinomialDistribution[n, {p_1, p_2, ..., p_m}] represents a multinomial distribution with n trials and probabilities p_i.

BinomialProcess[p] represents a binomial process with event probability p.

BernoulliGraphDistribution[n, p] represents a Bernoulli graph distribution for n-vertex graphs with edge probability p.

NegativeMultinomialDistribution[n, p] represents a negative multinomial distribution with parameter n and failure probability vector p.