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How many even, three-digit positive integers have the property that exactly two of the integer's digits are even?

 Apr 16, 2022
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There are 2 cases to consider: 

 

Even - Odd - Even

Odd - Even - Even

 

For the first case, there are \(4 \times 5 \times 5 = 100\) numbers. (Remember, the leading digit can't be 0!!)

 

For the second case, there are \(5 \times 5 \times 5 = 125\) numbers. 

 

Thus, there are a total of \(100 + 125 = \color{brown}\boxed{225}\) numbers that meet these criteria.

 Apr 16, 2022

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