document.write( "Question 639097: In how many ways can n + 1 men and n women be seated in a row under each of the following conditions:\r
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Algebra.Com's Answer #402555 by Edwin McCravy(20056)\"\" \"About 
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In how many ways can n+1 men and n women be seated in a row under each of the following conditions:
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document.write( "1) no restriction by sex\r\n" );
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document.write( "There are n+1 + n or 2n+1 people.  Answer (2n+1)!\r\n" );
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document.write( "2) no men in adjacent seats\r\n" );
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document.write( "The n+1 men go in the n+1 odd-numbered seats 1,3,5,7,...,n-1,n+1.\r\n" );
document.write( "That's (n+1)! ways to seat the men.  For each of those (n+1)! ways,\r\n" );
document.write( "the n women go in the n even-numbered seats 2,4,6,8,...n-2,n.\r\n" );
document.write( "That's n! ways to seat the women.\r\n" );
document.write( "That's (n+1)!n! \r\n" );
document.write( "That can also be written (n+1)n!n! = (n+1)(n!)²\r\n" );
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document.write( "3) at least two men in adjacent seats\r\n" );
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document.write( "[The answer to 1)] MINUS [the answer to 2)]\r\n" );
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document.write( "(2n+1)! - (n+1)!n!\r\n" );
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document.write( "Edwin
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