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Math Help - combinatorial question

  1. #1
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    combinatorial question

    Here is my question, I'm very confused. I struggle with word problems. Could someone please point me in the right direction?

    A store has 10 identical boxed stereos to store on 3 shelves. How many ways can the boxes be
    stored on the shelves if:

    (a) there are no restrictions on the number of stereos on each shelf?
    (b) the top shelf must have exactly 2 stereos on it?
    (c) each shelf must have at least 2 stereos on it?
    (d) no shelf can have more than 5 stereos on it?

    Greatly Appreciated.

    hmm for question (a)

    is 3x 10! correct?
    Last edited by yoonsi; October 15th 2009 at 12:58 AM.
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  2. #2
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    I think... after much confusion and struggling, that I have it for (a)

    is it: 12/ (10!)(2!) = 66?

    (b) 9!/(8!)(1!) = 9

    (c) 8!/(6!)(2!) = 28

    (d) (12/ (10!)(2!)) - (6!/(4!)(2!)) = 51

    this is what I got... *phew* I would appreciate it if someone could tell me if I did this right =]
    Last edited by yoonsi; October 15th 2009 at 02:44 AM. Reason: I think I worked it out =p
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  3. #3
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    yes! for (a) and (b)

    would you explain (c), (d)

    PS: plz refer to http://www.mathhelpforum.com/math-he...-question.html
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  4. #4
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    oh wait... (c) should be... (6!) / (4!)(2!)

    and now im not sure at all what I did for (d) =p help anyone?
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  5. #5
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    Quote Originally Posted by yoonsi View Post
    oh wait... (c) should be... (6!) / (4!)(2!)

    and now im not sure at all what I did for (d) =p help anyone?
    Hi - (c) yes

    (d) first find how many ways are there when at least one of the shelf has > 5 boxes (which is complement of what is asked in the question)

    1)observe there can be only 1 shelf with >5 boxes (this observation helps us greatly otherwise we would have to do something more complicated) - so in how many ways can you select the shelf with>5 boxes?

    2)once you are done with (1), put 6 boxes in the selected shelf (well it should at least have 6 (>5) boxes as per our argument!) - rest 4 can be distributed in anyways you like among the 3 shelves. How many? You have already solved this bit

    Combine (1) and (2) to find how many ways are there when at least one of the shelf has > 5 boxes

    Now that you have this ans - answering the original question should be straight fwd

    ill give you the final answer - 21 (if i'm not wrong in my calcs)

    Thanks
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  6. #6
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    Thanks so much,

    what I did was:
    (d) (12/ (10!)(2!)) - (6!/(4!)(2!)) = 51

    when I should have:
    (d) (12/ (10!)(2!)) - 3*(6!/(4!)(2!)) = 21

    Thanks =D
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