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Default counting unique items within categories

Hi, I've run into a little problem that I can't seem to figure out...

I have two columns of data - one column contains a list of items, and the
other contains one of three possible categories (A, B, or C) to which the
items are assigned. Due to other considerations within my sheet, specific
items may be repeated multiple times within the first column, and they may
also exist in any combination of all three categories.

My question is: Is there a way to summarize how many UNIQUE items exist
within each of the three categories (i.e., the number of different items
within category A, not including the repeats)?

I've tried lots of versions of the countif and frequency function, but
nothing has worked so far... thanks for your help!!

 
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