10th Asian Pacific Mathematics Olympiad 1998 Problems

10th Asian Pacific Mathematics Olympiad 1998 ProblemsA1.  S is the set of all possible n-tuples (X1, X2, ... , Xn) where each Xi is a subset of {1, 2, ... , 1998}. For each member k of S let f(k) be the number of elements in the union of its n elements. Find the sum of f(k) over all k in S.