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. $26^{2} \times10^{4}$
• B. $^{26}P_{2} \times^{10} P_{4}$
• C. $^{26}P_{2}\times9\times^{10}p_{3}$
• D. $26^{2}\times9\times10^{3}$

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