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A vehicle registration number consists of 2 letters of English alphabets followed by 4 digits, where the first digit is not zero. Then the total number of vehicles with distinct registration numbers is
  • a)
    262 x 104
  • b)
    26P2 x 10 P4
  • c)
    26 P2 x 9 x 10 P3
  • d)
    262 x 9 x 103
Correct answer is option 'D'. Can you explain this answer?
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To find the total number of vehicles with distinct registration numbers, we need to consider the different possibilities for each part of the registration number.

Let's break down the registration number into its components:

1. First Letter: There are 26 letters in the English alphabet. Since the first letter can be any letter from A to Z, there are 26 possibilities for the first letter.

2. Second Letter: Similarly, there are 26 possibilities for the second letter.

3. First Digit: The first digit cannot be zero, so there are 9 possibilities for the first digit (1 to 9).

4. Remaining Digits: The remaining 3 digits can be any digit from 0 to 9. So, there are 10 possibilities for each of the remaining digits.

To find the total number of vehicles, we multiply the number of possibilities for each part of the registration number:

Total number of vehicles = (Number of possibilities for the first letter) x (Number of possibilities for the second letter) x (Number of possibilities for the first digit) x (Number of possibilities for the remaining digits)

Total number of vehicles = 26 x 26 x 9 x 10 x 10 x 10

Simplifying the expression, we get:

Total number of vehicles = 26^2 x 9 x 10^3

Therefore, the correct answer is option 'D': 262 x 9 x 103.
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A vehicle registration number consists of 2 letters of English alphabets followed by 4 digits, where the first digit is not zero. Then the total number of vehicles with distinct registration numbers isa)262x 104b)26P2x10 P4c)26 P2x 9 x 10 P3d)262x 9 x 103Correct answer is option 'D'. Can you explain this answer?
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