- First digit cannot be zero and the repetition of digits is not allowed.
- The first-digit cannot be zero, but the repetition of digits is allowed?
This means the first digit can be selected from the 9 digits 1, 2, 3, 4 .... , 9 So, there are 9 ways of filling the first digit of the license plates.
Now, 9 digits are Ieft including 0. So, second place can be filled with any of the remaining 9 digits in 9 ways.
The third place of the license plates can be filled with in any of the remaining 8 digits. So, there are 8 ways of filling the third place.
The fourth place of the license plates can be filled with in any of the remaining 7 digits. So, there are 7 ways at filling the fourth place.
The last place of the license plates can be filled with in any of the remaining 6 digits. So, there are 6 ways of filling the fourth place.
Hence, the total number of ways = 9 × 9 × 8 × 7 × 6 = 27216
$\therefore$ First digit can be selected from the 9 digits 1, 2, 3 ..... , 9 So, there are 9 ways at filling the first digit of the licence plates.
The repetition of digits is allowed to made a license plates number.
$\therefore$ The number of ways to fill the remaining places of the number platas = 10 × 10 × 10 × 10.
Hence, the total number of ways = 9 × 10 × 10 × 10 × 10 = 90,000.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.