Combinatorics, Multinomial coefficients

If S is a set of n objects, and n1, n2, × × × , nk are non-negative integers satisfying n1 + n2 + × × × + nk = n, then the number of ways in which the objects can be distributed into k boxes, X1, X2, × × × , Xk, such that the box Xi contains exactly ni objects is given in terms of a ratio constructed of factorials (see 4). This number, called a multinomial coefficient, is the coefficient in the multinomial expansion of the nth power of the sum of the