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Count the rows in one range based on both a key and the existence of a value in another range

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This is likely a duplicate, but it's difficult to search for or to recognize when I have found it.

In Google Sheets, I want a formula for E1:E4 (pink) that will give me the count of rows in A1:B5 (blue) where the key ("Aaron") matches the the value in D and the value ("9/4/2023") exists in A7:A8 (yellow).

The result is the numbers shown, which I entered manually. I am looking for the simplest or most common approach. Thank you for any guidance!

A table matching the description in the question body


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