Question

What is the number of ways in which one can post $5$ letters in $7$ letter boxes?

• A. $7^5$
• B. $3^5$
• C. $5^7$
• D. $2520$

Answer 1

The correct option is A $7^5$

Each of the $7$ choices that could be made for the first letter there are $7$ choices that can be made for the second letter, and the choices multiply

There are $7\times 7$ possibilities for where the first $2$ letters will be placed, and for each of those cases,

There are $7$ possibilities for what to do with the third letter.

For each letter there are exactly $7$ choices,

and the number of possible outcomes is the product of all those $7^{\prime }s.$

The calculation done as $7\times 7\times 7\times 7\times 7=7^5$ is based on the fact that for each letter you have exactly $7$ choices

$\therefore$ Option A is correct