The number of ways to distribute 5 indistinguishable objects into 3 indistinguishable boxes is the number of partitions of 5 into at most 3 positive integers. Let's list all the possible partitions:
5;
4,1;
3,2;
3,1,1;
2,2,1;
Since all the possibilities are listed, there are 5 ways to distribute 5 indistinguishable objects into 3 indistinguishable boxes.
Answer: 5
Email: asuleime@purdue.edu
--Asuleime 03:34, 25 September 2008 (UTC)
Comments:
Good work on getting the correct answer; your explanation is short and to-the-point, and I liked how your restated the problem in terms of splitting 5 up. However, there were a couple things I would have liked to see in more detail:
(a) How did you come up with the list of partitions? It looks like you put them in some order, so I would guess that there's a reason behind it.
(b) How do you know that you have all of them? (Granted, it looks like you do, and I believe the answer is correct, but there's always that chance that there's something that wasn't considered that needed to be. Can you prove that you covered all your bases?)
Thomas34 01:02, 1 October 2008 (UTC)
Comments:
I liked the solution, it is simple and to the point. The only addition I would make is defining what a partition is so that people understand why the numbers have to be sorted in non-decreasing order.
--Nathan Claus 12:19, 5 October 2008 (UTC)
