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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
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Verified Answer
The correct answer is:
$26^{2} \times 9 \times 10^{3}$
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
$$
\begin{array}{l}
=26 \times 26 \times 9 \times 10 \times 10 \times 10 \\
=26^{2} \times 9 \times 10^{3}
\end{array}
$$
$$
=26 \times 26
$$
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
$$
\begin{array}{l}
=26 \times 26 \times 9 \times 10 \times 10 \times 10 \\
=26^{2} \times 9 \times 10^{3}
\end{array}
$$
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