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Math Help - Probability

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    Probability

    We are given 3 balls and 10 balls.

    a. Suppose the boxes and the balls are all distinguishable. How many ways are there to put 10 balls into the boxes.

    b. Suppose the boxes are indistinguishable, and the balls are also indistinguishable. How many ways are there to put 10 balls into the boxes?
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  2. #2
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    Quote Originally Posted by Koeppel1 View Post
    We are given 3 balls and 10 balls.

    a. Suppose the boxes and the balls are all distinguishable. How many ways are there to put 10 balls into the boxes.

    b. Suppose the boxes are indistinguishable, and the balls are also indistinguishable. How many ways are there to put 10 balls into the boxes?
    Part a) is no different from asking "How many function are there from a set of ten to a set of 3"?

    Part b) is more complicated. Here we must assume that at least one box is not empty. "How many ways can 10 be partitioned into three or fewer summonds"?
    Here are some examples. \boxed{10} \;;\;\boxed{9,1}\;;\boxed{8,1,1}\;;\;\boxed{7,2,1}  \text{ etc}.
    That is not an easy task.
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