How many even, three-digit positive integers have the property that exactly two of the integer's digits are even?
+2668 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.
