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Default sumproduct - multiple conditions

I want to get the sum of all transactions in my table of type "RI" or "II" or
"AI". I am also filtering for other conditions (warehouse and merchandise
class), but these conditions have only one option for each cell in my
spreadsheet. In other words, for each warehouse and merchandise class, I
need to show the sum total of those three types of transactions. I could do
something like this:

=SUMPRODUCT(--(<wh column=<wh),--(<type column="RI"),--(<merch
column=<merch),'<amt column)+SUMPRODUCT(--(<wh column=<wh),--(<type
column="II"),--(<merch column=<merch),'<amt column)+SUMPRODUCT(--(<wh
column=<wh),--(<type column="AI"),--(<merch column=<merch),'<amt column)

where everything in "<" is a cell or array reference. That is really long
and messy.

Is there a way to put an OR statement inside the SUMPRODUCT? Something
along the lines of changing "--(<type column="RI")" to "--(OR(<type
column="RI",<type column="II",<type column="AI"))" which doesn't work.
 
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