The following problem arises in quantum mechanics. Find the number of ordered triples of nonnegative integers a, b, c whose sum a+b+c is a given positive integer n. (For example, if n=2, we could have (a,b,c)=(2,0,0) or (0,2,0) or (0,0,2) or (0,1,1) or (1,0,1) or (1,1,0).) Hint: Show that this is the same as the number of distinguishable distributions of n identical balls in 3 boxes, and follow the method of Example 5, or use Problem 19(a).