Question

In how many ways can $3$ letters be posted in $4$ letters boxes so that all the letters are not posted in the same letter box?

Answer 1

We take a letter. It can be posted in any of the 4 boxes. Similarly, next letter can be posted in 4 ways, and so on. Total number = $4^3$

But there are 4 such cases in which each Box can contain all 3 letters

So, we have to remove 4 such cases

Hence, No of ways required $=4^3-4=64-4=60$