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Ok, try this:
Name, Cook, Baker
Jim, Yes, No
John, No, Yes
Julie, Yes, Yes
Joann, No, Yes

Now write an array formula to show how many people are both Cook and Baker, as simple as:
=COUNTIFS(B2:B5, "Yes", C2:C5, "Yes")

Probably you can do it, but I'm not familiar with the array formula, and I wonder if it will be this simple.