WBJEE2012MathematicsPermutation and CombinationActual
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
Options
- A26² 10⁴
- B²⁶ P ₂ ¹⁰ P ₄
- C²⁶ P ₂ 9 ¹⁰ P ₃
- D26² 9 10³
Correct answer
D. 26² 9 10³
Step-by-step solution
The total number of arrangements of 2 letters of English alphabet =26 26 The total number of arrangements of 4 digits number in which first digit is not zero =9 10 10 10 The total number of vehicles with distinct registration number array l =26 26 9 10 10 10 =26² 9 10³ array