Calulus 2 Counting Pie

Question

After another gym class you are taksed with putting the 14 identical dodgeballs away into 4 bins. This time, no bin can hold more than 6 balls. How many ways can you clean up?

Answer 1

If bins are identical, we can arrange them in decreasing order (by the number of dodgeballs).

The simplest way is just list all possible ways.

1. 6, 6, 2, 0
2. 6, 6, 1, 1
3. 6, 5, 3, 0
4. 6, 5, 2, 1
5. 6, 4, 4, 0
6. 6, 4, 3, 1
7. 6, 4, 2, 2
8. 6, 3, 3, 2
9. 5, 5, 4, 0
10. 5, 5, 3, 1
11. 5, 5, 2, 2
12. 5, 4, 4, 1
13. 5, 4, 3, 2
14. 5, 3, 3, 3
15. 4, 4, 4, 2
16. 4, 4, 3, 3

Totally there are 16 ways.