I was at dinner and we started discussing this problem:
4 people sitting in chairs at dinner, and various people leave to go to the bathroom.
How many total unique permutations are there of people sitting at the table if a unique permutation also depends on which chair you are sitting in (so a unique permutation depends on who is there, and which chair they are sitting in)
I'm not sure whether it would just be 2^4 (the number of combinations of people, including/excluding each of them) times 4! (the rotations in chairs) but then we were trying to figure out if this is over counting or under counting.