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 of putting all the balls in exactly one box$= 5$

As for each ball there are 5 choices for the box, the number of ways of putting balls in the boxes $= 5^5$

Thus, the required number of ways of putting the balls in the boxes $= 5^5 – 5$