Problem:
How many even integers are there between and whose digits are all different and come from the set ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Because the numbers are even, they must end in either or . If the last digit is , the first digit must be and thus there are four choices remaining for the middle digit. If the last digit is , then there are two choices for the first digit, either or , and for each choice there are four possibilities for the middle digit. The total number of choices is then .
The problems on this page are the property of the MAA's American Mathematics Competitions