The integer 203 has an odd ones digit, an even tens digit, and an even hundreds digit. How many integers between 100 and 999 have an odd ones digit, an even tens digit, and an even hundreds digit?
The integers between 100 to 999, inclusive, are exactly the three-digit positive integers. Consider three-digit integers of the form $a b c$ where the digit $a$ is even, the digit $b$ is even, and the digit $c$ is odd.

There are 4 possibilities for $a: 2,4,6,8$. (We note that $a$ cannot equal 0 .)

There are 5 possibilities for $b: 0,2,4,6,8$.

There are 5 possibilities for $c: 1,3,5,7,9$.

Each choice of digits from these lists gives a distinct integer that satisfies the conditions.

Therefore, the number of such integers is $4 \cdot 5 \cdot 5=100$.

ANSWER: 100

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