Question

In how many ways we can distribute 999 identical balls in 3 identical boxes??

Answer 1

Answer:

Hint: Break into 3 cases 1. all boxes have same num of balls 2. exactly 2 boxes have same num of balls 3. all boxes have different num of balls

Case 1 and 2 are trivial to solve Case 3: solve assuming boxes are different (this is a std combinatorics problem) . reduce that by number where you could permute the distribution across boxes across all the cases (as boxes are identical)

finally add the 3 cases off course