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Count with multiple column criteria and within date range

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Hi All

I am trying to get count of Resources Type (Capital or Operating) if row is within certain month as specified in the Metrics tab.

The uploaded sample includes 2 tabs - Resources and Metrics. Resources is a list of Person records and whether they are Capital or Operating. Each row has a Start Date and may have End Date. A person can existing multiple times if they have moved from Capital to Operating and vice versa. The second tab is metrics to count number of Persons by Capital or Operating in a given month.

The Resource list will include tens of thousands of rows, so the formula needs to be efficient.

What is the best formula?

Thanks.
 

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