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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?

 
 Apr 23, 2025
 #1
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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.

 Apr 26, 2025
 #2
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ok wait never mind the answer is 96 because I forgot it was a circle and so there’s symmetry meaning that instead of 4! it’s 3! and there is no clockwise nor counterclockwise because it’s a circle. so the real equation is 3!*2^4
 Apr 26, 2025

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