document.write( "Question 1073173: what is the soletion of in how many ways 7 man and 7 womenv can be seateted around table such that no two women can sit tgether \n" ); document.write( "
Algebra.Com's Answer #688600 by Edwin McCravy(20056)\"\" \"About 
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document.write( "The only way is to seat them alternating men and women,\r\n" );
document.write( "so no two men sit together either.  \r\n" );
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document.write( "Seat the 7 men first.\r\n" );
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document.write( "It would be 7! ways to seat the men, but we must divide\r\n" );
document.write( "by 7 since the table and people are assumed to be sitting on \r\n" );
document.write( "a turntable that can be rotated 7 different ways. Therefore \r\n" );
document.write( "7! counts the number 7 times too many, so there are 7!/7 or \r\n" );
document.write( "6! ways to seat the men.\r\n" );
document.write( "     \r\n" );
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document.write( "            M   \r\n" );
document.write( "       M         M\r\n" );
document.write( "                  \r\n" );
document.write( "      M           M\r\n" );
document.write( "                  \r\n" );
document.write( "         M     M\r\n" );
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document.write( "Now for each of those 6! circular permutations, there\r\n" );
document.write( "are 7 chairs in which to seat the 7 women. So they\r\n" );
document.write( "can be seated any of 7! ways.\r\n" );
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document.write( "         W  M  W\r\n" );
document.write( "       M         M\r\n" );
document.write( "      W           W\r\n" );
document.write( "      M           M\r\n" );
document.write( "       W         W  \r\n" );
document.write( "         M  W  M\r\n" );
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document.write( "So the answer is 6!7! = 3628800  ways.\r\n" );
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document.write( "Edwin
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