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Default calculating number of days (e.g., Mondays) between two dates

I need to count the number of days between a start date and end date and the
questions about this I found here don't seem to help (boggle me!) I need a
universal formula that will cover variable days which are listed in a
separate column:
G (rows) = names of days; J (rows) = start date; K (rows) = end date. On
top of this, I am sometimes having to count more than one day (up to three)
within a week (e.g., Mondays AND Fridays) which I'd be willing to put in
separate columns (i.e., columns G,H,I) if needed, but if only one column has
a day listed, the formula needs to ignore the empty columns.
A knotty problem?
 
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