In how many ways can you put 15 balls in 4 boxes such that each box contains an odd number of balls?
Details and Assumptions:
- All the balls are identical.
- All of the boxes should be considered identical. However, we can fit a box into another.
- For example, the image shows 3 boxes which contain 5 balls each, and 1 box which contains all 15 balls (and all 3 boxes).
Bonus: Generalize the given situation for \(m\) balls and \(n\) boxes.