In mathematics, the multinomial formula is an expression of a power of a sum in terms of powers of the addends. For any positive integer m and any nonnegative integer n, the multinomial formula is
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 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.
A multinomial is a mathematical expression consisting of two or more terms, e.g.
The multinomialtheorem provides the general form of the expansion of the powers of this expression, in the process specifying the multinomial coefficients which are found in that expansion.
This is version 9 of multinomialtheorem, born on 2002-12-07, modified 2005-01-02.
In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums.
The binomial theorem is mentioned in the Gilbert and Sullivan song I am the Very Model of a Modern Major General.
The binomial theorem appears in at least three different works by Monty Python - Coal Mine in Llandarogh Carmarthen, The Tale of Happy Valley, and The Meaning of Life.
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