Science Fair Project Encyclopedia
The summation is taken over all combinations of the indices k1 through km such that k1 + k2 + k3 + ... + km = n; some or all of the nonnegative indices may be zero. The numbers
are the multinomial coefficients.
The multinomial coefficients have a direct combinatorial interpretation, as the number of ways of depositing n distinguished objects in m bins, with k1 in the first, and so on. This is an equivalent assertion.
The binomial theorem and binomial coefficient are special cases, for m = 2, of the multinomial formula and multinomial coefficient, respectively. Therefore this is also called the multinomial theorem.
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details