document.write( "Question 1209104: How many ways are there to arrange 4 male students and 3 female students in 10 seats around a circle such that each gender sits together? \n" ); document.write( "

Algebra.Com's Answer #847675 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "In this case, you have actually a block of 4 males   with their 4 chairs,\r\n" );
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document.write( "                                a block of 3 females with their 3 chairs,\r\n" );
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document.write( "                                and the block of remaining 10-4-3 = 3 vacant chairs.\r\n" );
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document.write( "And you arrange these 1 + 1 + 1 = 3 blocks circularly around the circular table.\r\n" );
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document.write( "It gives you   = 2 distinguishable circular permutations  of 3 blocks.\r\n" );
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document.write( "In addition, you have  4! = 24 permutations inside the block of 4 males\r\n" );
document.write( "                  and  3! =  6 permutations inside the block of 3 females.\r\n" );
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document.write( "You do not permute vacant chairs inside the block of 3 vacant chairs,\r\n" );
document.write( "since vacant chairs are indistinguishable.\r\n" );
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document.write( "All this gives you  2 * 24 * 6 = 288 distinguishable circular permutations.\r\n" );
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