Problem:
What is the average (mean) of all -digit numbers that can be formed by using each of the digits , and exactly once?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Each digit appears the same number of times in the 's place, the 's place, ..., and the 's place. The average of the digits in each place is
Hence the average of all the numbers is
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions