How many different even four-digit numbers can you make without using the same digit more than once in each of the numbers?
Solution:
For the number to be even you need to use one of the five even digits (0, 2, 4, 6, or 8) in the ones place.
Once you have chosen a digit for the ones place you can use any of the remaining nine digits in the tens place.
Then you can choose any of the remaining eight digits for the hundreds place, and any of the seven left after that for the thousands place.
There are 5 x 9 x 8 x 7, or 2520 different even four-digit numbers that do not use the same digit more than once.