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?

Accepted Solution

Answer: There are 17576000 ways to generate different license plates.Step-by-step explanation:Since we have given thatNumbers are given = 0 to 9 = 10 numbersNumber of letters = 26We 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[tex]26\times 26\times 26\times 10\times 10\times 10\\\\=26^3\times 10^3\\\\=17576\times 1000\\\\=17576000[/tex]Hence, there are 17576000 ways to generate different license plates.