How many ways can you distribute 4 identical balls among 4 different boxes?
We know we have the groups
4-0-0-0, 3-1-0-0, 2-2-0-0, 2-1-1-0, and 1-1-1-1.
There are 4 ways for 4-0-0-0 to be arranged,
4 for 3-1-0-0, 4c2 = 6 for 2-2-0-0, and 4*3 and 1 for 2-1-1-0, and 1-1-1-1, respectively
SO we have 35