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Math Help - partitioning in a number of groups

  1. #1
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    partitioning in a number of groups

    Someone know how to compute in how many ways is it possible to partition a collection of M indistinguishable elements in I groups (evidently with at least one element for each groups)???
    The groups are distinguishable; I mean, if M=3 and I=2 the solution is 2 combinations (1,2) and (2,1) (whereas (3,0) and (0,3) are not allowed since a group is empty)

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  2. #2
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    {{M-1}\choose{I-1}}
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  3. #3
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    Thank you very much...
    and admitting also an indefinite number of "empty" groups within the total number of groups I? so, in the same example of above, if M=3 and I=2 the solution is 4 combinations: (3,0), (2,1), (1,2), (0,3).
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  4. #4
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    Allowing for groups to be empty: {{M+I-1}\choose{M}} .
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  5. #5
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    the last question...I hope
    is there also a simple form for to give an answer to the previous two posts in the case of distinguishable elements?
    So, the number of combinations of M distinguishable elements in I distinguishable groups, with and without admitting for empty groups.
    For example, if M=2 and I=2:
    - without admitting for empty groups: (obj_1, obj_2), (obj_2, obj_1) == 2 combinations.
    - admitting empty groups: (obj_1, obj_2), (obj_2, obj_1), (obj_1 \& obj_2, nothing), (nothing, obj_1 \& obj_2) == 4 combinations.

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