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Distributing presents

  1. Oct 16, 2008 #1
    1. The problem statement, all variables and given/known data

    in how many ways can one distribute 15 identical gifts between 10 distinct children?


    2. Relevant equations

    (n + k - 1, k - 1) bionomail coeff.

    3. The attempt at a solution

    n = 15, k = 10

    (24, 9) = 24!/(9!*15!)

    It would be much appreciated if someone can verify my result. Thanks.
     
  2. jcsd
  3. Oct 17, 2008 #2

    Mark44

    Staff: Mentor

    I don't think what you have is right. I think the total number of ways is the sum of the binomial coefficients
    (15 0) + (15 1) + (15 2) + ... + (15 10) where each one is n!/[(n - k)! k!]

    My reasoning is this:
    (15 0) - the number of ways to give all 15 gifts to no one--1 way
    (15 1) - the number of ways to give all 15 gifts to 1 child--15 ways
    (15 2) - the number of ways to give 15 gifts to 2 children (and hence none to the other 8)
    And so on.
    Anyway, that's how I would approach this problem.
     
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