The results of Section C in the main text are not correct if there is a significant probability that two systems will occupy the same state simultaneously. Show this for the following simple case. Suppose that there are two subsystems (i.e., two particles) and the same two accessible states for each (i.e., two "boxes"). If both subsystems may occupy the same state, how many different arrangements of the system are there if the two subsystems are
(a) distinguishable,
(b) identical?
(c) Do these two answers differ by a factor 2!.