First slide

Permutations

Question

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

Moderate

A

$5^{5} - 5$
B

$5^{5} - 10$
C

$2^{2} - 2$
D

none of these

Solution

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 $= 5^{5} - 5$

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