IN REPLY TO POST #7 (A try to help you with your thought, Hoping I can)
Sumifs can be used for multiple criteria in the same array column, PROVIDED all the criteria turns to be true for the output to come. I mean the multiple criteria used within Sumifs, should all be true together to give you the desired result.
In the formula you have used to get the output, all are providing the correct result except the that used in cell A10 and A15, because the criteria you have used within the sumifs can't be true at the same time. Even the formula
=SUMPRODUCT(SUMIFS(B1:B7,A1:A7,A9,A1:A7,B9))
will give you zero as a result, because as I mentioned two criteria can't be true at the same time in this data, if cell contains "A", it can't contain "C".
In short Sumifs treat the criterias as within AND operation.
However as mentioned by Aladin, the formula used by him, treats both criteria as one, an array is being used and so as mentioned by him, two inputs are fed to sumifs together and later sumproduct is used to do the total of the two inputs.
If I am understanding wrong then more clarifications are welcome.