1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Combinatorial Methods

  1. Sep 5, 2010 #1
    1. The problem statement, all variables and given/known data

    If k people are seated in a random manner in a circle containing n chairs (n>k), what is the probability that the people will occupy k adjacent chairs in the circle?

    3. The attempt at a solution

    1) The total probability of k people seated in a circle of n chairs is [ (n "choose" k) = p1 ]

    2) The amount of people occupying k adjacent chairs. We have (n-k) total unoccupied chairs. For a small chunk of the total number, (Kth Person, 1st Person, 2nd Person are all seated next to each other) or (2nd Person, 1st Person, Kth Person seated adjacently). => (n-k+2)=p2 total ways to seat adjacently (considering the two identical orders).

    3) Solution = p2*p1 = (n-k+2) / (n "choose" k)
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted