SOLUTION: 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

Algebra.Com
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

RELATED QUESTIONS

There are 6 children riding on the roller coaster. Each car holds 6 in 3 rows of 2 seats... (answered by edjones)
A theater has 30 rows of seats with 20 seats in each row. Tickets for the seats in the... (answered by edjones)
A group of 30 people consists of 15 women and 15 men. How many ways are there to (a)... (answered by ikleyn)
In how many ways can n + 1 men and n women be seated in a row under each of the following (answered by Edwin McCravy)
A roller coaster can hold 48 people. there arev46 on the ride younger adults fill 1/3 of... (answered by rothauserc)
A theater has 32 rows of seats. The first row has 24 seats. Each of the remaining rows... (answered by scott8148)
Suppose that there is a large group of people, consisting of exactly 2N women and 2N men. (answered by stanbon)
a roller coaster has room for 10 people. the people sit single file, one after the other. (answered by solver91311)
An amphitheater has a number of rows with 30 seats in the first row, 32 in the second, 34 (answered by ikleyn,greenestamps,solver91311)