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Math Help - Another ''36 sweets'' counting problem ???

  1. #1
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    Another ''36 sweets'' counting problem ???

    This is similar to a problem that I've already posted here before. Infact its the second part to that problem. I decided to start a new thread. Apologies if I should haved added it to the existing thread.

    36 sweets are to be divided among 6 individuals. How many ways can they be divided such that each individual receives at least 3 AND no more than 7 sweets?

    Any hints as to how this problem should be solved would be appreciated.
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  2. #2
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    This is not a straightforward counting question.
    It can easily be done with generating functions.

    Go to this website.

    The coefficient of x^{36} is the answer to the question.
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  3. #3
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    426?

    Thats much smaller than what I've calculated. I tried doing the question and got 15,946 ways. (Although how I got this number is an altogether different discussion :P)
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  4. #4
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    Quote Originally Posted by Markhor View Post
    426?
    Thats much smaller than what I've calculated. I tried doing the question and got 15,946 ways. (Although how I got this number is an altogether different discussion :P)
    But you must remember that the at most seven really complicates it answer.
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