Grieve (grieve) wrote,

Math puzzle

I ran across this problem today, and I feel like it must have been solved before, but I am not sure where to look. Suppose you have X objects and Y buckets. The question is how many unique ways can I distribute the X objects into the Y buckets.

For example if I have 2 objects and 3 buckets I can distribute the two objects as follows:
2 0 0
0 2 0
0 0 2
1 1 0
1 0 1
0 1 1

Which gives me six unique ways to distribute the objects.

With 3 objects and 3 buckets there are 10 ways to do it. My question is what is the algorithm given X and Y which will give you all unique combinations?
Tags: math

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