sum of all possible combinations

I have a worksheet where the columns represent types of medication and the rows are individual people.

I need to total how many people have each combination of 12 medications. For example, how many have the combination of med1, med2 and med10; or the combination of med2, med5, med6, med7 and med8; etc. Just examples.

See attached partial data file (hope it uploaded).

Thanks for any advice, really appreciate the help!