In how many ways can 4 balls be placed in 3 boxes if the balls are distinguishable, and the boxes are indistinguishable?
+44 This question is similar to yours, I suggest looking at this link: https://web2.0calc.com/questions/in-how-many-ways-can-4-balls-be-placed-in-4-boxes, if you have any questions just ask :)
Since the boxes are indistinguishable, we have the following 4 situations:
4 - 0 - 0, and there is only 1 option
3 - 1 - 0, and it is choose 1 out of 4, which has 4 options
2 - 2 - 0, and it is choose 2 out of 4, which has 6 options
2 - 1 - 1, and it is choose 2 out of 4, which has 6 options
The answer is then 1 + 4 + 6 + 6 = 17.
