Question

In how many ways can 5 letters be posted in 4 letter boxes?

Answer 1

Hint: We will use the fundamental principle of counting to solve the problem. We will start by finding the ways in which a letter can be posted. Then we will find the total ways in which 5 letters can be posted.

Complete step-by-step answer:
Now, we have been given to find the ways in which we can post 5 letters in 4 letter boxes.
Now, we have the letter boxes be represented as square box below,
$\ \ \$
Now, for each letter there are 4 ways to go to any of the letter boxes as a letter can handle more than one letter simultaneously. So, we have for each letter the ways it can be posted as 4.
Now, we know that by fundamental principle of counting we can multiply each case to find the total ways as,
$\begin{aligned} & 4\times 4\times 4\times 4\times 4 \\\ & ={{4}^{5}} \\\ \end{aligned}$
Hence, the number of ways in which 5 letters can be posted in 4 letter boxes is ${{4}^{5}}$.

Note: It is important to note that we have used a basic fundamental principle of counting to count the total number of possible outcomes in a situation. In this principle if we have n ways of doing one thing after and m ways of doing other things after first, then there are $n\times m$ ways of doing both things together.