A state's license plate number consists of 3 digits followed by 2 letters. If the digit 0 and the letter X cannot be used, how many distinct possible licence plate numbers are possible?
There are 9 choices for each of the first three digits, and 25 choices for the last two digits.
Use the multiplication rule to get:
93252
To calculate the number of distinct possible license plate numbers, you need to determine the count of available options for each digit/letter position and then multiply them together.
In this case, we have the following restrictions:
- The first digit can be any digit from 1 to 9, excluding 0. So there are 9 options for the first digit.
- The second digit can be any digit from 0 to 9, excluding 0. So there are 9 options for the second digit.
- The third digit can be any digit from 0 to 9, excluding 0. So there are 9 options for the third digit.
- The first letter can be any letter from A to Z, excluding X. So there are 25 options for the first letter.
- The second letter can be any letter from A to Z, excluding X. So there are 25 options for the second letter.
Now, we can multiply these options together to find the total number of distinct possible license plate numbers:
Total = 9 options for the first digit × 9 options for the second digit × 9 options for the third digit × 25 options for the first letter × 25 options for the second letter
Total = 9 × 9 × 9 × 25 × 25 = 182,250
Therefore, there are 182,250 distinct possible license plate numbers.