document.write( "Question 342369: ten people, 5 men and 5 women, are to be seated in a row of 10 chairs. What is the probability that the men and women end up in alternate chairs?
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Algebra.Com's Answer #245191 by Edwin McCravy(20054) $\"\"$ $\"About$

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document.write( "First we find the numerator of the probability.\r\n" );
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document.write( "The number of ways we can have this arrangement\r\n" );
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document.write( "M W M W M W M W M W\r\n" );
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document.write( "For each of the 5! ways to place the men there are 5! ways to place the\r\n" );
document.write( "women. That's 5!*5! or (5!)²\r\n" );
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document.write( "But we could also have this arrangement:\r\n" );
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document.write( "W M W M W M W M W M\r\n" );
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document.write( "which is another (5!)²\r\n" );
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document.write( "So the numerator, which is the number of ways to have men and women in\r\n" );
document.write( "alternate seats, is 2(5!)²\r\n" );
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document.write( "The denominator is the number of ways anybody can sit anywhere, which\r\n" );
document.write( "is 10!\r\n" );
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document.write( "So the probability is\r\n" );
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document.write( "Edwin

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