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stumped
 
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Default Counting in arrays

After reading a lot of answers in this group I am still stuck with
this one.

I have 4 excel columns thus:-

date initials date initial

03/01/2004 JK 05/02/2001 jw
23/05/2004 AP 12/12/2004 aw
I wish to count cells where the month and the year and the initials
are set conditions.

eg Count all JKs in january 2004
I can count on the first 2 columns with

{=SUM(IF(MONTH('2004'!$P$3:$P$998)=1,IF(YEAR('2004 '!$P$3:$P$998)=2004,IF('2004'!$R$3:$R$998="jk",1,0 ))))}

but cannot work out how to include next 2 columns.
The layout of the spreadsheet cannot be changed.
Go easy on me as I'm a pensioner trying to help a grand daughter