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Default COUNTIF or SUMPRODUCT with Mulitple Criteria

I have a survey where each row represents a different question. The top three
rows record the race and gender of respondents, e.g. the answers in Row 2 are
"W" "B" or "L" or White, Black or Latino and the answers in Row 3 are "M" or
"F" for male or female. IN the remaining rows, the answers are either "1" or
"0" for "Yes" or "No" answers to questions.

I want to create a formula that will count the number of yes or no answers
accounting for race and gender--in other words, where multiple criteria are
met. For example, how many people that answered Yes to question X are Black
or White, or Black Women in particular. My inclination is to use COUNTIF, but
I have never done multiple criteria with COUNTIF. I have also seen SUMPRODUCT
recommended for this type of formula.

Any ideas would be much appreciated.
 
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