Excel/Math question

I don't understand your question at all. Can you give an example?

Okay. A student takes one course from each category, for a total of 6 courses. That same student may find that they can take 1 course that counts for two of the categories because it is listed under more than one category, meaning that they might only take 5 courses.

If there are 925 courses overall, 650 when all duplicates are eliminated, how many unique combinations of courses are possible across all 6 categories?

Keep in mind that taking course A, course B, and course C is the same as taking course B, course C, and course A. Only unique combinations are needed. I think using the formula N!/K! * (N-K)!, or COMBIN(650,6), will do that - but I'm not a mathematician and I am still trying to figure it out. My concern is the use of 6 for K in the formula forcing 6 combinations where they might not be needed, although using the unduplicated number of courses may solve that problem.

Does that help?

I think you need to solve the problem in parts and total the result, and there will be a lot or parts:

Take one class non-overlapping class from each category, or,

Take one class that covers two categories and one non-overlapping class each from the other five, or

Take one class that covers two categories, one class that overlaps two other categories, and one non-overlapping class each from the other four, or

...


Or, generate all 250 choose 6 combinations and discard those that redundantly cover any categories.

No easy way, no.

And what would you do if you had such a list? Where would you store the resulting 600TB file if Excel could create one?

This would be a good time for the academician to buy a book on combinatorics