Question

In how many ways can $mn$ letters be posted in $n$ letter boxes?

• A. ${\left(mn\right)}^n$
• B. $m^{mn}$
• C. $n^{mn}$
• D. None of these

Answer 1

The correct option is C

$n^{mn}$

Find the number of ways to posting $mn$ letters into $n$ letter boxes :

A letter chosen can be posted in any of $n$ boxes.

Similarly, every letter can be posted in any of $n$ boxes.

So, the total number of ways for posting $mn$ letters into $n$ letter boxes is given by :

$$\begin{gathered} \Rightarrow n\times n\times n\times ........(mntimes) \\ \Rightarrow n^{mn} \end{gathered}$$

Hence, option (C) is the correct answer.