If a class of 10 students has five men, how many ways can the men and

If no two men sit next to each other, a man must sit between two women. Since there are an equal number of men and women, it must be true that no two women are sitting to each other also (because a woman must sit between two men also). In other words, the men and women sit alternately next to each other. Since we have a circular arrangement, we use the circular permutations formula, and so the number of ways to arrange the 5 men is (5 - 1)! = 4!. However, since there are 5 seats remaining, the number of ways to arrange the women is 5!. Thus, the total number of ways the men and women can be arranged in a circle so that men and women sit alternately next to each other is 4! x 5!.

Answer: A