Saturday, November 20, 2004

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


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