1. **State the problem:** We want to find how many integers between 100 and 999 have an odd ones digit, an even tens digit, and an even hundreds digit. 2. **Analyze the digits:** - Hundreds digit: must be even and between 1 and 9 (since the number is between 100 and 999). - Tens digit: must be even and between 0 and 9. - Ones digit: must be odd and between 0 and 9. 3. **Determine possible values for each digit:** - Hundreds digit (even and 1 to 9): possible digits are 2, 4, 6, 8 (4 options). - Tens digit (even 0 to 9): possible digits are 0, 2, 4, 6, 8 (5 options). - Ones digit (odd 0 to 9): possible digits are 1, 3, 5, 7, 9 (5 options). 4. **Calculate total number of such integers:** $$\text{Total} = 4 \times 5 \times 5 = 100$$ 5. **Final answer:** There are **100** integers between 100 and 999 with an odd ones digit, an even tens digit, and an even hundreds digit.