Question

A vehicle registration number consists of $2$ letters of English alphabet followed by $4$ digits, where the first digit is not zero. Then the total number of vehicles with distinct registration numbers is

• A. $26^2\times 10^4$
• B. ${}^{26}{P}_2{\times }^{10}{P}_4$
• C. ${}^{26}{P}_2\times 9{\times }^{10}{p}_3$
• D. $26^2\times 9\times 10^3$

Answer 1

Answer: (D)

The total number of arrangements of 2 letters of English alphabet
$=26\times 26$
The total number of arrangements of 4 digits number in which first digit is not zero
$=9\times 10\times 10\times 10$
$\therefore$ The total number of vehicles with distinct registration number
$=26\times 26\times 9\times 10\times 10\times 10$
$=26^2\times 9\times 10^3$