An 'Odd' Arrangement

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.

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