Question 85120: The Board of Directors does not have assigned seats in the conference room. If there are 12 of them, seated at a round table, how many different seating arrangements are possible?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The Board of Directors does not have assigned seats in the conference room. If there are 12 of them, seated at a round table, how many different seating arrangements are possible?
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Permutations on a Circle
Arrangements are also often made in a circle—we no longer have a left end and a right end. Now our first element placed merely provides a point of reference instead of having n choices. Thus with n distinguishable objects we have (n-1)! arrangements instead of n!.
Example: Consider arranging the letters ABCD. There are 4!=24 such arrangements. If considered as a circular arrangement there are but 3!=6 arrangements.
Often in circular arrangements only betweenness and not clockwise/counterclockwise is what matters. This further reduces the arrangements by a factor of 2.
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Your Problem:
# of arrangements = 11! = 39,916,800
Cheers,
Stan H.
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