document.write( "Question 945075: A roller coaster car has n rows of seats, each of which had room for two people. If n men and n women get into the car with a man and woman in each row, in how many different ways may the car be filled? \n" ); document.write( "
Algebra.Com's Answer #576289 by Edwin McCravy(20056)\"\" \"About 
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document.write( "First for each row we choose whether a man will\r\n" );
document.write( "sit on the left and a woman on the right, or whether\r\n" );
document.write( "a woman will sit on the left and a man on the right.\r\n" );
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document.write( "We choose this seating arrangement for the 1st row in 2 ways.\r\n" );
document.write( "For each of those, we choose this seating arrangement for \r\n" );
document.write( "the 2nd row also in 2 ways.\r\n" );
document.write( "For each of those, we choose this seating arrangement for \r\n" );
document.write( "the 3rd row also in 2 ways.\r\n" );
document.write( "...\r\n" );
document.write( "For each of those, we choose this seating arrangement for \r\n" );
document.write( "the (n-1)st row also in 2 ways.\r\n" );
document.write( "For each of those, we choose this seating arrangement for \r\n" );
document.write( "the nth row also in 2 ways.\r\n" );
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document.write( "That's 2n ways to choose for every row whether\r\n" );
document.write( "a man will sit on the left and a woman on the right or\r\n" );
document.write( "vice-versa.\r\n" );
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document.write( "Then we can seat the n men in the n designated men's seats in\r\n" );
document.write( "n! ways.\r\n" );
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document.write( "Then we can seat the n women in the n designated women's seats \r\n" );
document.write( "also in n! ways.\r\n" );
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document.write( "Answer: 2nŚn!2\r\n" );
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document.write( "Edwin
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