2005 AMC 10B Problems/Problem 20
What is the average (mean) of all -digit numbers that can be formed by using each of the digits 1, 3, 5, 7, 8 and exactly once?
We first look at how many times each number will appear in each slot. If we fix a number in a slot, then there are ways to arrange the other numbers, so each number appears in each spot times. Therefore, the sum of all such numbers is Since there are such numbers, we divide to get