Solution:
The number of ways of putting all the balls in exactly one box
As for each ball there are 5 choices for the box, the number of ways of putting balls in the boxes
Thus, the required number of ways of putting the balls in the boxes
The number of ways we can put 5 different balls in 5 different boxes such that at most three boxes is empty, is equal to
The number of ways we can put 5 different balls in 5 different boxes such that at most three boxes is empty, is equal to
