document.write( "Question 331931: find the number of ways to seat n married couples around a table in the following cases
\n" ); document.write( "1/ men and women are alternate
\n" ); document.write( "2/ every woman is next to her husband
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Algebra.Com's Answer #237953 by galactus(183) $\"\"$ $\"About$

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Seat the n women around the table in (n-1)! ways. The n men are then seated in the n spaces between the women in n! ways.\r
\n" ); document.write( "\n" ); document.write( "Thus, there are $\"n%21%28n-1%29%21\"$ ways to seat the men and women alternating.\r
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\n" ); document.write( "\n" ); document.write( "Tie each married couple together and pretend they are one person.\r
\n" ); document.write( "\n" ); document.write( "We can seat them in (n-1)! ways. Now, since each couple can be switched around in 2 ways, there are 2^n ways to arrange all of them\r
\n" ); document.write( "\n" ); document.write( "So, there are $\"%28n-1%29%21%2A2%5En\"$ ways to arrange the couples with the women sitting with their husbands.\r
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