"There are 10 distinct balls that can be put into two identical urns such that no urn is empty. How many ways can that be done?"
I know how to do this question when the urns are distinct (its simply 9 choose 1), but when the urns are identical the first urn containing only 1 ball and the second urn containing 9 balls is the same thing as the first containing 9 balls and the second containing 1 ball. How do I take account for all the double counting?
Also, is there a more general formula that can account for any n number of identical urns?