The sumproduct is an array formula that can validate multiple criteria and the resulting array of TRUE and FALSE can be converted to 1s and 0s and then summed up to give final count.
How to use SUMPRODUCT function to validate a criteria and sum
Using Sumproduct to check for multiple criterias
Category: Math and trigonometry
Returns the sum of the products of corresponding array components
SUMPRODUCT(array1, [array2], [array3], ...)
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