I recently encountered a real-life scenario where I need to enumerate all the possible combinations. The problem could be framed as follows:
Suppose there are 14 identical balls and 5 unique bins that can hold 6 balls each. What are the total number of ways to place the 14 balls into the 5 bins?
Using a divide and conquer strategy (basically I first look at what happens when there are only 2 unique bins, then 4 unique bins, and finally 5), I manage to come up with an upper bound of 3060. But I have no idea how to handle the constraint that each bin can only hold 6 balls.