There are 5 possible groupings:
0 0 5 - 1
0 1 4 - 5
0 2 3 - 10
1 1 3 - 10
1 2 2 - 20
For a total of 46 possibilities. I don't see a more general formula for this. Because [A][B][C] and [B][A][C] are same, the boxes are indistinguishable that proves.
As a result, 5 orders to indicate 5 indistinguishable objects into 3 indistinguishable boxes.
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grader's comment : good job. I also got the same answer for the question!
-- by lee462 10:48, 5 October 2008 (UTC)
