document.write( "Question 1210194: 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? \n" ); document.write( "

Algebra.Com's Answer #851529 by ikleyn(52782) $\"\"$ $\"About$

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\n" ); document.write( "At a meeting, two scientists, two mathematicians, two historians, and two artists are to be seated around a circular table.
\n" ); document.write( "In how many ways can they be seated so that all four pairs of people from the same discipline are seated together?
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\n" ); document.write( "\n" ); document.write( "        Since you came with pairs of persons around a round table, it means (at the normal teaching process)\r
\n" ); document.write( "\n" ); document.write( "        that you are just familiar with the basic cases for such problems.\r
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\n" ); document.write( "\n" ); document.write( "        So, I will not repeat the basics, but will simply give a short form solution.\r
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document.write( "In this problem, we have 4 pairs as the units/items.\r\n" );
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document.write( "4 items can be placed around a circle in (4-1)! = 3! = 6 different way (circular permutations).\r\n" );
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document.write( "In addition, one permutation is possible inside each pair.\r\n" );
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document.write( "It gives, in total,    = 16*6 = 96  different circular placements in this problem.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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