Question

How many different license plates are possible if a license plate consists of 2 capital letters followed by 5 digits?

Answer 1

`26\cdot26\cdot10\cdot10\cdot10\cdot10\cdot10=\\ 26^2\cdot10^5=\\ 676\cdot 10000=\\ 67600000`

Answer 2

The first letter can be any one of 26 letters. For each one . . .
The second letter can be any one of 26 letters. For each one . . .

The first digit can be any one of 10 digits. For each one . . .
The second digit can be any one of 10 digits. For each one . . .
The third digit can be any one of 10 digits. For each one . . .
The fourth digit can be any one of 10 digits. For each one . . .
The fifth digit can be any one of 10 digits.

The total number of possibilities is

(26 x 26 x 10 x 10 x 10 x 10 x 10) =

( 26² x 10⁵) = (676 x 100,000) = 67,600,000 .