Problem:
How many even integers between and have four different digits?
Solution:
We first count those integers of the desired type with or as the thousands digit. In this case, the thousands digit can be chosen in ways, and then the units digit , or can be chosen in ways. There are then choices for the hundreds digit and then for the tens digit. Thus there are integers of the type we seek with or as the thousands digit. Similarly, if the thousands digit is , we have even integers with four different digits. Thus we have a total of integers.
The problems on this page are the property of the MAA's American Mathematics Competitions