How many ways are there to distribute five indistinguishable objects into 3 indistinguishable boxes?
Good question. Here's your answer.
Since the objects and boxes are all indistinguishable, this problem becomes relatively simple. The situation with 5 objects in one box is unique. This means that the scenarios (with the first number being the number of boxes in the first box, etc.) of:
(5-0-0), (0-5-0), (0-0-5)
are identical. In a similar fashion, these box situations are identical:
(4-1-0), (4-0-1), (1-4-0), (1-0-4), (0-4-1), (0-1-4).
So it follows that the only options are:
(5-0-0) (4-1-0) (3-2-0) (3-1-1) (2-2-1)
Hence, 5 ways. --Dakinsey 11:54, 24 September 2008 (UTC)
