A state makes auto license plates that have two letters (excluding I, 0, and Q) followed by four digits of which the first digit is not zero. How many different license plates are possible?

4,761,000

10950300

To find the number of different license plates possible, we need to multiply the number of options for each part of the license plate format.

1. Number of options for the first letter: There are 26 letters in the English alphabet, but we need to exclude I, O, and Q. So, there are 26 - 3 = 23 options.
2. Number of options for the second letter: Similarly, there are 26 - 3 = 23 options.
3. Number of options for the first digit: Since the first digit cannot be zero, there are 9 options (1-9).
4. Number of options for the second, third, and fourth digits: Each of these digits can be any number from 0 to 9, so there are 10 options for each digit.

Now, we can multiply the number of options together to find the total number of different license plates possible:

Number of options = (23 possibilities for the first letter) × (23 possibilities for the second letter) × (9 possibilities for the first digit) × (10 possibilities for the second digit) × (10 possibilities for the third digit) × (10 possibilities for the fourth digit)

Number of options = 23 × 23 × 9 × 10 × 10 × 10

Calculating the expression, we get:

Number of options = 11,070,000

Therefore, there are 11,070,000 different license plates possible.

To calculate the number of different license plates possible, we need to consider the number of possibilities for each component of the license plate.

Let's break it down:

1. For the first letter: Since the state excludes the letters I, O, and Q, there are 26 letters in the English alphabet minus 3 excluded letters, so there are 26 - 3 = 23 possibilities.

2. For the second letter: Similarly, there are 23 possibilities, as we cannot repeat the first letter.

3. For the first digit: Since the first digit cannot be zero, there are 9 possibilities (from 1 to 9).

4. For the second, third, and fourth digits: Each digit has 10 possibilities (from 0 to 9).

Now, multiply the number of possibilities for each component:

23 (possibilities for the first letter) * 23 (possibilities for the second letter) * 9 (possibilities for the first digit) * 10 (possibilities for each of the second, third, and fourth digits) = 23 * 23 * 9 * 10 = 47,070 different license plates are possible.