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Homework Help: 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


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    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?
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