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Default how many times a particular day of the week appears in a given month

Hello - I'm building a spreadsheet that is supposed to calculate how
many times a particular day of the week appears in the month for a
billing letter. Students are scheduled for a lesson on one of the days
of the week, and based on that day, I want to count how many times that
day appears in a given month and calculate their bill. For example,
there are 5 Tuesdays, Wednesdays and Thursdays in July 2006, but only 4
Fridays, Saturdays, Sundays and Mondays. I've got a column for the
date, and another column for the day (Monday, Tues. etc.) Is there some
function in Excel that would help do this or a formula or algorithm?
Thanks!

 
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