A) if both objects and boxes and indistinguishable
B) if objects are indistinguishable and boxes are distinguishable
I know there are n! ways to but n objects into n boxes (both distinguishable).
A) I also know that to put n indistinguishable objects into n indistinguishable boxes we must count the number of partitions of n into n integers. I am unsure of how to calculate this and how to add the 1 box empty condition.
B) I know there are C(n + r − 1, n − 1) ways to place n indistinguishable objects into r distinguishable boxes. I can replace r with n. I am unsure of how to account for the 1 box empty condition here, as well.