Question

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

• A. $63$
• B. $60$
• C. $77$
• D. $81$

Answer 1

The correct option is B

$60$

Explanation for the correct option:

Finding the number of ways in which the letters can be posted in letter boxes:

There are $3$ letters and $4$ letter boxes.

Each letter can be posted in all the $4$ letter boxes.

So one letter can be posted in $4$ ways.

Therefore, $3$ letters can be posted in: $4\times 4\times 4=4^3$ ways

Now, the given condition is that all the letters are not posted in the same letter box,

then the possible number of ways becomes $$\begin{gathered} =4^3-4 \\ =60 \end{gathered}$$

Hence, Option (B) is correct.