How many ways are there to put 5 balls in 2 boxes if the balls are not distinguishable and neither are the boxes?
I was thinking (5,0), (4,1), and (3,2) for a total of 12 ways. Any help is greatly appreciated.
2026-03-27 19:54:14.1774641254
How many ways are there to put 5 balls in 2 boxes if the balls are not distinguishable and neither are the boxes?
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It is 3: the partitions of 5 into $\leq 2 $ parts. These are pretty much just the tuples you have listed: (5), (4,1), (3,2).