WBJEE · Maths · Permutation Combination
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 \({ }^{26} \mathrm{P}_{2} \times{ }^{10} \mathrm{P}_{4}\)
- C \({ }^{26} \mathrm{P}_{2} \times 9 \times{ }^{10} \mathrm{P}_{3}\)
- D \(26^{2} \times 9 \times 10^{3}\)
Answer & Solution
Correct Answer
(D) \(26^{2} \times 9 \times 10^{3}\)
Step-by-step Solution
Detailed explanation
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…
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