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Default COUNTIF or SUMPRODUCT with multiple criteria

I have a survey where Yes and No answers are signified by "1" or "0" in a
series of rows (each row corresponding to a different question in the survey)
and where race of respondent is indicated by "B" (for Black), "W" (White) or
"L" (for Latino" in one of the rows. I want to create a formula that counts
the number of occurrences of "1" in a range of cells in one row where "B" (or
W or L) occurs in a cell range in another row. In other words, where both
criteria are met--e.g. how many Black people answered Yes to a particular
question, how many white people answered No to a particular question, etc.

My inclination is to use COUNTIF but I am not clear if such a formula is
possible with multiple criteria. I have never used SUMPRODUCT, but I have
seen that recommended on these forums.

Any ideas?
 
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