Regarding problem 4 grading on PS1

If you used factorials in this problem to account for indistinguishibility of particles, i.e (V/v)^N / N! instead of just (V/v)^N, and got half a point taken off, see Sophia and you can get that half point back if you want. The N! doesn't affect the problem, because the number of particles is constant throughout (only volumes are changing). The true quantum mechanical result is that the N! should be in there, we just hadn't really gotten to that yet in class.