Question

A hotel reservation number consists of 5 digits, followed by 2 letters, followed by 2 digits. How many different reservation numbers are possible?

Answer 1

Answer:

$6,760,000,000$

Explanation:

Note that there are 10 digits (0 - 9) and there are 26 letters of the alphabets (A - Z)

We're told that the reservation number consists of 5 digits, followed by 2 letters, followed by 2 digits, we can go ahead and determine how many different reservation numbers are possible assuming that the numbers can be repeated as seen below;

$\begin{gathered} 10\times10\times10\times10\times10\times26\times26\times10\times10 \\ =10^5\times26^2\times10^2 \\ =100000\times676\times100 \\ =6,760,000,000\text{ } \end{gathered}$