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: Basic combinations problem

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data

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

    I realize that there are n choose k sets of k seats to be occupied, and that there are n-k+1 sets of k adjacent seats. So the probability that I'm looking for is:

    (n-k+1)/(n choose k)

    What I don't understand is how the above probability simplifies to:


    Can someone please explain? Thanks.

    2. Relevant equations

    (nk) = n choose k = n!/[(n-k)!k!]

    3. The attempt at a solution

    (n-k+1)/(n choose k) = [(n-k+1)(n-k)!k!]/n!

    Not sure what to do from here.
  2. jcsd
  3. Apr 27, 2010 #2
    Look at (n-k+1)(n-k)!, can you simplify this product any?
    Last edited: Apr 27, 2010
  4. Apr 27, 2010 #3
    Other than finding a quotient, I've never had to manipulate/simplify factorials. Thinking about this again, since the number (n-k+1) is 1 greater than the number (n-k), (n-k)! times (n-k+1) must equal (n-k+1)!.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook