Determine the number of different license plates possible if the first letter must be an N , M , or P and repetition of letters and numbers is not permitted.
A license plate is to consist of 3 letters followed by 3 digits. Determine the number of different license plates possible if the first letter must be an N , M , or P and repetition of letters and numbers is not permitted.
To determine the number of different license plates possible given the conditions, we need to consider the choices for each character position.
First, we know that the first letter must be an N, M, or P. Let's begin with this condition.
1. For the first letter:
- There are 3 options (N, M, or P).
Next, we move on to the remaining characters.
2. For the second letter:
- Since repetition is not permitted, there are 25 options (excluding the letter chosen for the first position).
3. For the third letter:
- Again, there are 25 options (excluding the two letters used in the first two positions).
4. For the fourth letter:
- Similarly, there are 24 options (excluding the three letters used in the previous positions).
5. For the first digit:
- There are 10 options (0-9) since repetition is not permitted.
6. For the second digit:
- Again, there are 9 options (excluding the digit used in the fifth position) since repetition is not allowed.
To determine the total number of possible license plates, we multiply the number of choices at each position:
Total = 3 (First letter) * 25 (Second letter) * 25 (Third letter) * 24 (Fourth letter) * 10 (First digit) * 9 (Second digit)
Total = 3 * 25 * 25 * 24 * 10 * 9
Therefore, the number of different license plates possible, given the conditions, is 1,620,000.