This problem can be generalized similarly to find the coefficients of  they are called multinomial coefficients. It can readily be shown that the coefficient of  in the expansion of  is

where, of course, the sum  of the exponents must be n.

Another interesting problem, and one with frequent applications, is that of finding the number of ways in which one can arrange a set of objects in a row, that is, the number of permutations of the set. Let us consider the set of four objects a, b, c, d. They can be arranged in the following ways:
 

Rather than write them all out, if we are only interested in the number of arrangements, we may think of the problem thus: We have four spaces to fill. If we put, for example, the b in the first, we have only the a, c, and d to choose from in filling the remaining three. And if we put the d in the second, we have only a and c for the remaining; and so forth. So we have four choices for the first space, three for the second, two for the third, and one for the fourth. This gives us  or 4! arrangements of four objects. This argument can be used to show that there are n! arrangements of n objects.