OK, so we need to put 5 indistinguishable objects into 3 indistinguishable boxes.
The easiest way to do this is to just list the different possibilities.
5 0 0 4 1 0 3 2 0 3 1 1 2 2 1
Each column is a box and each row is a possibility. Notice that I did not label the boxes, this is because they are indistinguishable. This makes it so I do not have to list 5-0-0, 0-5-0, and 0-0-5 as separate possibilities. They are all the same. Also, options like 4-1-0 only has one possibility because the objects are also indistinguishable so it doesn't matter which object is separate from the others.
Add up these possibilities and we get 5 ways.
kduhon 10:38 24, September 2008 (UTC)
