Question

An auto license plate consists of 6 digits; the first three are any letter (from the 26 alphabets), and the last three are any number from 0 to 9. For example, AAA 000, ABC 123, and ZZZ 999 are three possible license plate numbers. How many different license plate numbers may be created?

Answer 1

Answer: There are 17576000 ways to generate different license plates.

Step-by-step explanation:

Since we have given that

Numbers are given = 0 to 9 = 10 numbers

Number of letters = 26

We need to generate the license plate numbers.

Since there are repetition allowed.

We would use "Fundamental theorem of counting".

So, the number of different license numbers may be created as given as

$26\times 26\times 26\times 10\times 10\times 10\\\\=26^3\times 10^3\\\\=17576\times 1000\\\\=17576000$

Hence, there are 17576000 ways to generate different license plates.