How many ways can you distribute 4 identical balls among 4 identical boxes?
Since the balls are the same and the boxes are the same, the problem is basically how many ways can you get a sum of 4.
1+1+1+1
1+1+2
2+2
3+1
4
I get 5 ways.
Four(4) Identical balls and Four(4) identical boxes mean that the balls are indistinguishable and the boxes are also indistinguishable...
Since there is no restriction, let's try number separation.
1+1+2+0
2+2+0+0
1+3+0+0
4+0+0+0
Five(5) ways are possilbe.
Thank you!