Multinomial Theorem

The multinomial theorem describes how to expand a power of a sum of several terms, generalizing the binomial theorem from two terms to any number of terms. For a sum of m terms raised to the nth power, it expresses the expansion as a sum of terms with multinomial coefficients of the form n factorial divided by the product of the factorials of the individual exponents, which must themselves sum to n, and the theorem reduces to the ordinary binomial theorem when m equals 2; it has applications in combinatorics, probability and polynomial algebra, including counting arrangements of objects into bins and permutations of words with repeated letters. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/