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Question: Answered & Verified by Expert
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
MathematicsPermutation CombinationWBJEEWBJEE 2012
Options:
  • A $26^{2} \times 10^{4}$
  • B ${ }^{26} \mathrm{P}_{2} \times{ }^{10} \mathrm{P}_{4}$
  • C ${ }^{26} \mathrm{P}_{2} \times 9 \times{ }^{10} \mathrm{P}_{3}$
  • D $26^{2} \times 9 \times 10^{3}$
Solution:
2375 Upvotes 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
$$
\begin{array}{l}
=26 \times 26 \times 9 \times 10 \times 10 \times 10 \\
=26^{2} \times 9 \times 10^{3}
\end{array}
$$

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