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Default countif for two ranges?

Example:

I'd like to use COUNTIF to alnalyze the following two ranges and come
up with a formula that would spit out how many times joe is green. And
then modify it for joe meeting a blue condition, mary meeting green,
blue, etc. Is this possible? From what I've been reading COUNTIF can't
compare two ranges? Is a macro the only way to go here?

Any help would be appreciated.


column A Column B
joe green
mary green
joe blue
joe blue
joe green
mary blue
joe green
mary green
mary green

 
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