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Homework Help: People seated in a circle

  1. Dec 4, 2005 #1
    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
     
  2. jcsd
  3. Dec 4, 2005 #2

    LeonhardEuler

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    Gold Member

    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.
     
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