+479 How many ways are there to put 4 balls in 3 boxes if the balls are distinguishable but the boxes are not?
With no restrictions and empty boxes are allowed, you have:
[4 + 3 - 1 ] nCr [3 - 1] = 6 C 2 = 15 ways.
This is a case of of 4 distinct balls into 3 identical boxes: Case 1 uses “Stirling Numbers of the 2nd kind”. Case 2 uses “Bell numbers”
Case 1:
If we consider that ALL the Boxes Should have Balls, the Solution is: = 6 ways
Case 2:
If we consider that Boxes Can be left Empty, then the Solution is:
=0 + 1 + 7 + 6 = 14 ways
