CSMC 2023 Part A - Question 2, CEMC UWaterloo

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This problem is tagged with csmc, csmc23, highschool.

(Canadian Senior Mathematics Contest 2023, Part A, Question 2, CEMC - UWaterloo)

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?

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