round table permutation

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tRNA

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a problem in topscore says: how many arrengments can six people be seated round a circular table?
they said answer should be 120, (6-1)!=120 because you keep the position of one person constant!!! but why would you do that and the problem doesn't even tell us to do that, i see nothing special about the round table thing, I think the answer should be 720 if you do the regular permutation (6!), am i correct or are they correct??

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Well by the looks of things, if everyone were to move a seat over in a clockwise fashion, they would still be sitting in the same seating arrangement. Thus it doesn't matter what CHAIRS they sit in - it matters who they sit next to, and in what order (Tim sitting to the left of Jim who sits to the left of Bob is different from Tim sitting to the right of Jim who sits to the right of Bob).

The first person to sit down can choose any chair because they are all 'equal'. If they were arranged linearly, they wouldn't be equal since two chairs would be on the end and four in the middle.

So you arbitrarily choose a chair to start at, and any of the 6 can sit down. Then you look at the next chair over. Any of the remaining 5 can sit down. That leads you to 6!. But since all 6 chairs are equal, you divide your answer by 6. That's how you get 120.
 
thanks for replying streetwolf I get the idea that all the seats are equal but still why do you divide by 6??
 
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