Problem:
How many even three-digit integers have the property that their digits, read left to right, are in strictly increasing order?
Answer Choices:
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E.
Solution:
Let the integer have digits , and , read left to right. Because , none of the digits can be zero and cannot be 2 . If , then and must each be chosen from the digits 1,2 , and 3 . Therefore there are choices for and , and for each choice there is one acceptable order. Similarly, for and there are, respectively, and choices for and . Thus there are altogether such integers.
The problems on this page are the property of the MAA's American Mathematics Competitions