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    Question Occupany problem




    This is a homework problem that deals with occupancy.

    Q: consider r indistinguishable balls and n cells where n > r. The r balls are placed at random into n cells (multiple occupancy is possible). What is the probability P that r balls appear in r preselected cells (one to a cell)?

    As we have n > r, there are many empty spaces.

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    Re: Occupany problem

    Would you be able to solve the problem if the balls were distinguishable from one another?
    I don't have emotions and sometimes that makes me very sad.

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    Re: Occupany problem

    Unfortunately, No.
    All r balls are indistinguishable. it would be easy for distinguishable.

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    Re: Occupany problem

    I usually approach a problem like this by starting with a trivial case, say 2 balls and three cells. What are the possible outcomes?

    *** *** *** OXX XOX XXO
    OOX OXO XOO OXX XOX XXO

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    Re: Occupany problem

    Quote Originally Posted by asterisk View Post
    I usually approach a problem like this by starting with a trivial case, say 2 balls and three cells. What are the possible outcomes?

    *** *** *** OXX XOX XXO
    OOX OXO XOO OXX XOX XXO

    This would only work if a cell would take only one ball.
    but our case here, it is possible to have multiple balls in one cell.

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    Re: Occupany problem

    Which part are you having difficulty with? Calculating the size of the numerator or the denominator (or both)?
    I don't have emotions and sometimes that makes me very sad.

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    Re: Occupany problem


    Quote Originally Posted by Dason View Post
    Which part are you having difficulty with? Calculating the size of the numerator or the denominator (or both)?
    the numerator

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