document.write( "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?\r
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Algebra.Com's Answer #61345 by stanbon(75887) $\"\"$ $\"About$

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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?\r
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\n" ); document.write( "Permutations on a Circle
\n" ); document.write( "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!.
\n" ); document.write( "Example: Consider arranging the letters ABCD. There are 4!=24 such arrangements. If considered as a circular arrangement there are but 3!=6 arrangements.\r
\n" ); document.write( "\n" ); document.write( "Often in circular arrangements only betweenness and not clockwise/counterclockwise is what matters. This further reduces the arrangements by a factor of 2.\r
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\n" ); document.write( "Your Problem:
\n" ); document.write( "# of arrangements = 11! = 39,916,800
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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