A group contains n men and nwomen. 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 Pn, n) = n! arrangements are allowed for both men and women. There are n men and n women, and all of the an, n) = 2n! arrangements are allowed for both men and women. O 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!)?ways. O O