The answer on that page (by CPhill) is wrong however:
Ball splits Ways to distribute the balls
7 1 2
6 2 2
5 3 2
4 4 1
2 * 2 * 2 * 1 = 8 ways
but you cannot multiply as these are separate cases; you add them to get 7.
Then the answer would be 75.
There is also another way (stars and bars):
Choose 3 boxes to be empty: \({5 \choose 3}=10\)
Use stars and bars allowing empty boxes to calculate (or just count like CPhill)
CPhills method if he was here:
Ball splits
0 8
1 7
2 6
3 5
4 4
5 3
6 2
7 1
8 0
to get 9 different cases (stars and bars would be \({n+k-1 \choose k-1}={8+2-1\choose 2-1}={9\choose 1}=9\) ways)
Multiply by 10 to get 90 ways. However, this overcounts (0 0 0 8 0 is counted four times, and so are all other permutations) so we subtract 5*3=15 from 90 to get our final answer, 75.
