Problem:
How many integers between and have four distinct digits?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The thousands position can be filled by the digits through is excluded). Without repetition, the hundreds position can be filled with any of the remaining digits (including . Similarly without repetition, the tens position and ones position can be filled with the remaining and digits, respectively. Thus there are integers between and that have distinct digits.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions