If a class of 10 students has five men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?	Answers:
A) 5!4!
B) 5!5!
C) 4!4!
D) 10!
E) 10!/5!
Let's say that we make a man sits in spot 1. Then, a man must also sit in spots 3, 5, 7, 9. There are 5! ways of arranging the man this way. However, since this is a table (ie: circle), there are 5 ways where the initial man can sit, so we must divide 5! by 5, which equals to 4!.   It follows that a woman must sit in spots 2, 4, 6, 8, 10. There are 5! ways to arrange this.   Therefore, we get 4!5!. So the answer is 5!4!) 5!4!
<result>A</result>
If a class of 10 students has five men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?