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