Results 1 to 4 of 4

Math Help - How many ways can candy be distributed?

  1. #1
    Newbie
    Joined
    Sep 2011
    Posts
    6

    How many ways can candy be distributed?

    The question is, if there are 30 pieces of candy, and 20 babies. How many ways can the candy be divided amongst the babies such that all of the candy has been given out?

    My initial thought is that, we could obviously give 30 pieces to a single baby, thus there are 20 options there. Next we can give 29 to a single baby and one to every other. So there would be 19 combinations for every baby with 29. Thus 19 times 20 options? I can't seem to come up with a function for this. Help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1

    Re: How many ways can candy be distributed?

    Quote Originally Posted by mathmansam View Post
    The question is, if there are 30 pieces of candy, and 20 babies. How many ways can the candy be divided amongst the babies such that all of the candy has been given out?
    Assume that the pieces of candy are identical for this purpose.
    The number of ways to put N identical objects into K different cells is:
    \binom{N+K-1}{N}=\frac{(N+K-1)!}{N!(K-1)!}

    N is the number of candies and K here will be the number of children.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2011
    Posts
    6

    Re: How many ways can candy be distributed?

    Thank you! I realized that this was able to be solved with the above equation or n+k-1Ck-1 moments after posting. Love it here!!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1

    Re: How many ways can candy be distributed?

    Quote Originally Posted by mathmansam View Post
    Thank you! I realized that this was able to be solved with the above equation or n+k-1Ck-1 moments after posting. Love it here!!
    Here is something confusing to note.
    If the candies are all different then the answer is
    20^{30}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: October 23rd 2009, 02:57 AM
  2. normally distributed
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 6th 2008, 01:40 AM
  3. candy, weights, distributions, yum
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 15th 2008, 08:48 PM
  4. Boxes of Candy
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: January 14th 2007, 06:30 AM

Search Tags


/mathhelpforum @mathhelpforum