COUNTIFS avoiding double counting

Hi,

I have a spreadsheet that is set up basically as follows:

1: Gender
2: Age Group
3: Red
4: Green
5: Yellow
6: Orange
7: Any of the above

I'm trying to count all the favorite colors controlling for gender and age group, but some survey respondents selected a multiple favorite colors and/or any of the above. What is the best way to count this without double counting? I'm trying to count the number of men age 20-30 whose favorite color is anything EXCEPT Red.

Thanks!