A group contains n men and n women. Identify the steps used to find the number of ways to arrange n men and n women in a row if the men and women alternate? Assume the row has a distinguished head. There are n men and n women, and all of the P(n, n) = n! arrangements are allowed for both men and women. There are n men and n women, and all of the C(n, n) = 2n! arrangements are allowed for both men and women. Since the men and women must alternate, hence there should be same number of men and women. Therefore there are exactly two possibilities: either the row starts with a man and ends with a man or else it starts with a woman and ends with a woman. Therefore there are exactly two possibilities: either the row starts with a man and ends with a woman or else it starts with a woman and ends with a man. Arrange the men with women in between them, arrange the women with men in between them, and decide which sex starts the row. By the product rule, there are n! n! 2 = 2(n!)^2 ways