Question: Suppose we want to arrange p things of one type and q things of another type into a line.
(a) Argue that the p things can act as unlabeled balls and the q things can form separators between labeled boxes. How many ways are there to line up all the things?
(b) Argue that the q things can act as unlabeled balls and the p things can form separators between labeled boxes. How many ways are there to line up all the things?
(c) Aside from the fact that we are counting the same situation in two different ways, why do we get the same answer? (That is, give a symbolic explanation.)