At a meeting, two scientists, two mathematicians, two historians, and two artists are to be seated around a circular table. In how many ways can they be seated so that all four pairs of people from the same discipline are seated together?
I’m pretty sure the answer is 768 because you have 4 pairs so thats 4! ways to arrange and then you have to account for the fact that the two people in each pair can switch so thats x2 but that can be said for all four pairs so its *2^4 and then you have to account for the rotation cause it could be clockwise or counterclockwise so thats another *2. So the equation at the end is 4!*2*2^4 which is 768.