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?
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
First for each row we choose whether a man will
sit on the left and a woman on the right, or whether
a woman will sit on the left and a man on the right.
We choose this seating arrangement for the 1st row in 2 ways.
For each of those, we choose this seating arrangement for
the 2nd row also in 2 ways.
For each of those, we choose this seating arrangement for
the 3rd row also in 2 ways.
...
For each of those, we choose this seating arrangement for
the (n-1)st row also in 2 ways.
For each of those, we choose this seating arrangement for
the nth row also in 2 ways.
That's 2n ways to choose for every row whether
a man will sit on the left and a woman on the right or
vice-versa.
Then we can seat the n men in the n designated men's seats in
n! ways.
Then we can seat the n women in the n designated women's seats
also in n! ways.
Answer: 2nŚn!2
Edwin
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