1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: People seated in a circle
  1. The circle (Replies: 2)

Loading...