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!

Probability - Cominations and Integer Valued Vectors

  1. May 28, 2009 #1
    This problem comes from Sheldon Ross's book "A First Course in Probability (6th ed)."

    There are 5 hotels in a certain town. If 3 people check into hotels in a day, what is the probability that they each check into a different hotel?


    Attempt at a solution:

    There are 5C3 = 10 different combinations of hotels where each individual person picks a different hotel.

    I also decided that there were 7C4 = 35 possible ways for 3 individuals to choose from the 5 hotels, if more than 1 can stay in the same hotel. I got this answer because there are (n+r-1)C(r-1) distinct nonnegative integer-valued vectors (x1,x2,...,xr) satisfying x1 + x2 + ... + xr = n, where n = 3 and r = 5.

    Therefore, I got 10/35 as my answer, but the answer is actually .48 (rounded?)

    Interestingly, I got very close this answer mistakenly at first by dividing 5C3 by 7C2.
     
  2. jcsd
  3. May 28, 2009 #2
    Your'e making it too complicated

    [tex] \frac {P(5,3)}{5^{3}} [/tex]
     
  4. May 28, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The first person arrives and checks into any hotel. The second person arrives and checks into a hotel. What is the probability that person checks into a different hotel? The third person arrives. What is the probability this person checks into yet a different hotel? The probability that they check into three different hotels is the product of those two probabilities.. This is exactly the same as Random Variable gives- although, Random Variable, it would be better not to just "give" answers. Especially in the "coursework and homework sections".
     
  5. May 28, 2009 #4
    Wow, I'm embarrassed.

    Thanks guys!

    BTW, is there any way to do it the way that I was doing it?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Probability - Cominations and Integer Valued Vectors
Loading...