54. How many ways are there to distribute five indistinguishable objects into three indistinguishable boxes?
A: Similarly to everyone else, I just made a table for the possible situations.
5 - 0 - 0
4 - 1 - 0
3 - 2 - 0
2 - 2 - 1
1 - 3 - 1
These are all 5 possible cases. There would be more cases for each entry, such as on the top line (5,0,0) (0,5,0) (0,0,5). But because these are indistinguishable boxes, you only count one of the three cases per possibility.
The answer is 5.
--Mike Schonhoff 16:09, 24 September 2008 (UTC)
Great work, Mike! This is what I did, so obviously I agree... Since there's no explicit formula, I think this is probably the best way to handle a problem like this, especially since the numbers are small enough to be manageable. --Tmsteinh 09:34, 2 October 2008 (UTC)
