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

The correct option is D ${26}^2\times 9\times {10}^3$

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
$=26\times 26\times 9\times 10\times 10\times 10$
$={26}^2\times 9\times {10}^3$