permutation and combination question?

How many ways are there to distribute 40 identical marbles among 4 children without restriction

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  • Brian
    Lv 7
    9 years ago
    Favorite Answer

    There would be (43 C 3) = 43!/(40!*3!) = 12341 ways to distribute the marbles.

    This is the same as the number of solutions to the equation w + x + y + z = 40,

    where w, x, y and z are all integers greater than or equal to 0. Let each marble

    be represented by an o and let the + signs be the dividers between the collection

    of marbles each child ends up with. Then every distribution of marbles will be

    an arrangement of 40 o's and 3 +'s, and there are (40+3)! / (40!*3!) = (43 C 3)

    such arrangements.

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