Let a set of random variates X_1, X_2, ..., X_n have a probability function P(X_1 = x_1, ..., X_n = x_n) = (N!)/( product_(i = 1)^n x_i !) product_(i = 1)^n θ_i^(x_i) where x_i are nonnegative integers such that sum_(i = 1)^n x_i = N, and θ_i are constants with θ_i>0 and sum_(i = 1)^n θ_i = 1. Then the joint distribution of X_1, ..., X_n is a multinomial distribution and P(X_1 = x_1, ..., X_n = x_n) is given by the corresponding coefficient of the multinomial series (θ_1 + θ_2 + ... + θ_n)^N.
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