SUM the COUNT of values between dynamically specified columns and at a specified row

Hi all,

So in the attached anonymous example, what I want to see is the total number of "A"s against whatever resource is specified in cell I2:I3 and between (and including) whatever dates are specified in cells H2 and H3.

In the example I have attached I would expect the result to be 2, because there is an "A" in both cells C2 and D2.

However if I change the resource name lookup in I2:I3 from 'John Smith' to 'Adam John', I would expect the result to change to 1, because there is only one A in cells B3:D3.

I'm guessing this will require some kind of array formula but I can't figure it out! Any help would be greatly appreciated!!

Cheers,

Chris