document.write( "Question 388463: can you answer this and I will be greatful
\n" ); document.write( "Ten women and their husbands are to be seated on two sides of a long rectangular table, ten on each side. How many possible seating arrangements are there if
\n" ); document.write( "a) all the women sit on the same side?
\n" ); document.write( "b) women and men alternate along the able and every women sits opposite a man?
\n" ); document.write( "c) everyone sits opposite of their spouse?
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Algebra.Com's Answer #274896 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
can you answer this and I will be greatful
\n" ); document.write( "Ten women and their husbands are to be seated on two sides of a long rectangular table, ten on each side. How many possible seating arrangements are there if
\n" ); document.write( "a) all the women sit on the same side?
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document.write( "There are 2 possible configurations they can be placed, gender-wise\r\n" );
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document.write( "WWWWWWWWWW     MMMMMMMMMM\r\n" );
document.write( "MMMMMMMMMM  or WWWWWWWWWW\r\n" );
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document.write( "We have 10 women to POSITION 10 ways, that 10 Position 10 or 10P10 or 10! \r\n" );
document.write( "For each of those 10! ways to position the women on the left, there are\r\n" );
document.write( "10! ways to position the 10 men on the right.  That's (10!)².\r\n" );
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document.write( "Then for each of the 10! ways to place the women, there are 10! ways\r\n" );
document.write( "to place the men.  So for each of the above seating types there are (10!)²\r\n" );
document.write( "ways.\r\n" );
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document.write( "Since there are two kinds of configurations, the total number of ways is \r\n" );
document.write( "twice that, or 2(10!)² or about 26336378880000 ways.\r\n" );
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\n" ); document.write( "b) women and men alternate along the table and every women sits opposite a man?
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document.write( "There are 2 possible ways they can be placed, gender-wise\r\n" );
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document.write( "WMWMWMWMWM     MWMWMWMWMW\r\n" );
document.write( "MWMWMWMWMW  or WMWMWMWMWM\r\n" );
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document.write( "Each one the 10 women can be positioned 10 ways, that's 10P10 or 10!.\r\n" );
document.write( "For each of those 10! ways to place the women, there are also 10P10 ways\r\n" );
document.write( "to place the men.  So for each of the above two seating types there are \r\n" );
document.write( "(10!)² ways.\r\n" );
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document.write( "Since there are two kinds of seating types gender-wise, the total number of\r\n" );
document.write( "ways is twice that, or 2(10!)² or about 26336378880000 ways.\r\n" );
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\n" ); document.write( "c) everyone sits opposite of their spouse?
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document.write( "We can choose the leftmost couple any of 10 ways and there are 2 ways to\r\n" );
document.write( "place this couple, so that's 10*2 or 20 ways to choose and seat a left-most\r\n" );
document.write( "couple.\r\n" );
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document.write( "For each of the 10*2 ways to place the 1st (leftmost) couple, we can choose the\r\n" );
document.write( "2nd couple just to the right of the 1st couple any of 9 ways and there are 2\r\n" );
document.write( "ways to place this couple, so that's 9*2 or 18 ways to place the second couple\r\n" );
document.write( "from the left.  So that's a total of 10*2*9*2 ways to place the first two\r\n" );
document.write( "couples on the far left.\r\n" );
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document.write( "We can continue this process, and we will end up with:\r\n" );
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document.write( "10*2*9*2*8*2*7*2*6*2*5*2*4*2*3*2*2*2*1*2 =  10!*210 = 3715891200 ways.\r\n" );
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document.write( "Edwin
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