Multinomial Coefficient. Nk the following examples illustrate how to calculate the multinomial coefficient in practice. The covariance matrix is as follows.
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K j frac n k 1. The multinomial coefficients n 1 n 2 n k n 1 n 2 n k n 1 n 2 n k 1 are the terms in the multinomial series expansion. Displaystyle n choose k 1 k 2.
The multinomial coefficients the multinomial coefficient is widely used in statistics for example when computing probabilities with the hypergeometric distribution.
The multinomial coefficient is used to tell us the number of ways n in which n elements can be split into k disjoint subsets when the order of the elements in them does not matter. In other words the number of distinct permutations in a multiset of k distinct elements of multiplicity n i 1 i k is n 1 n k. Note that just like the binomial distribution the coefficients must sum to 1 this is the origin of the name multinomial distribution. A multinomial coefficient describes the number of possible partitions of n objects into k groups of size n1 n2 nk.
