we have the following question for homework:
N of the knights of the round table are having dinner. In how many ways can they sit around the table? What if Jack won't sit next to John and the queen - how many possible ways exist now?
The first question for quite easy - (n-1)!. I'm struggling with the second one: If Jack refuses to sit next to one of them I can count them as one, calculate and then subtract it from the total number of permutations. Its a little harder when he refuses to sit next to two people, because they CAN sit next to each other.
Also, how can I think of it in term of equivalence classes? I am trying to adopt this way of thinking so a hint in that direction would be nice. Thanks in advance!