document.write( "Question 1209098: In how many ways can 6 people be arranged to sit around a circular table with 10 chairs? \n" ); document.write( "

Algebra.Com's Answer #847678 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "In how many ways can 6 people be arranged to sit around a circular table with 10 chairs?
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document.write( "Working with circular placing/arrangements, we can think that the chairs are numbered from 1 to 10 inclusive, \r\n" );
document.write( "and that the chair number 1 is vacant and is placed in position \"North\" or {12 o'clock\".\r\n" );
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document.write( "Then we have 9 chairs from 2 to 10 to place there 6 people.\r\n" );
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document.write( "    1st person can be placed to any of 9 chairs            (9 options);\r\n" );
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document.write( "    2nd person can be placed to any of 8 remaining chairs  (8 options);\r\n" );
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document.write( "    3rd person can be placed to any of 7 remaining chairs  (7 options);\r\n" );
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document.write( "    4th person can be placed to any of 6 remaining chairs  (6 options);\r\n" );
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document.write( "    5th person can be placed to any of 5 remaining chairs  (5 options);\r\n" );
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document.write( "    6th person can be placed to any of 4 remaining chairs  (4 options).\r\n" );
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document.write( "Thus the total number of different placements/arrangements is this product\r\n" );
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document.write( "    9*8*7*6*5*4 = 60480.    ANSWER\r\n" );
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document.write( "It is the product of 6 consecutive integers in decreasing order, starting from 9.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved and explained.\r
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\n" ); document.write( "\n" ); document.write( "It can be solved/presented/explained in several different ways.
\n" ); document.write( "I chose this way since it explains everything from \"first principles\".\r
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