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Default Counting occurences of a specific day between two dates

Is there a formula that can count the occurences of a specific day between to
dates? I am familiar with an array formula
(=SUM((WEEKDAY(DATE(YEAR(N2),MONTH(N2),ROW(INDIREC T("1:"&DAY(DATE(YEAR(N2),MONTH(N2)+1,0))))))=B4)*1 )
that will count the number of times a specific day will be in a month, but I
need for two dates that I set. .My goal is to be figure out how many days a
month employees have worked up to a certain point in the month, but I cannot
use =NETWORKDAYS because we work Saturdays too, but not Sundays. Any help
will be greatly appreciated. Thank you.
 
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