What Is the Probability of Specific Seating Arrangements at a Round Table?

[jackbauer]

Hi people, was wondering if anyone could help me with this problem.
n men and m women are seated at a round table with exactly n+m places. What is the probability any given man has a woman immediately to his right. Also, what is the probability that a woman has a man to either side of her? I figured from combinatorics that the number of ways of seating these people in total is (n+m-1)! but I'm not sure how to proceed from here, anyone offer some assistance,
thanks,
Jack

 

[LeonhardEuler]

As far as the first question goes, if I understand it correctly, then it is pretty simple. There are n men and m women. So we want to know the probability that a woman is to the right of some given man. Well, there are m women and (n-1) men and each has an equal probability of being seated next to the man. So the probability is just the ratio of women to men. Am I understanding this problem correctly?

For the second part, the probability that a woman has a man to either side of her is the probability that a man is to her right plus the probability that a man is to her left, and then, since the chances of a man being on both sides has been counted twice, minus the probability that men are on both sides.