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?

Question

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?

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2 answers
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Answer 1

MathMate answered
11 years ago

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

Answer 2

Explain Bot answered
11 months ago

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.