A license plate is to have 3 digits followed by 2 uppercase letters. What is the number of different license plates possible if repetition of numbers and letters is not permitted?

Can we start with zero?

if so, then number of plates
=10x9x8x26x25 = 468000

If we can't start with a zero
= 9x9x8x26x25 = 421200

To find the number of different license plates possible without repetition of numbers and letters, we can break down the problem into two parts: counting the options for the digits and counting the options for the uppercase letters.

Part 1: Counting the options for the digits
Since repetition is not permitted, we can choose the first digit from 10 options (0-9). After choosing the first digit, we have 9 options left for the second digit, and 8 options left for the third digit. So, the number of options for the digits is 10 * 9 * 8 = 720.

Part 2: Counting the options for the uppercase letters
Since repetition is not permitted, we can choose the first uppercase letter from 26 options (A-Z). After choosing the first letter, we have 25 options left for the second letter. So, the number of options for the uppercase letters is 26 * 25 = 650.

To find the total number of different license plates possible, we multiply the number of options for the digits by the number of options for the uppercase letters: 720 * 650 = 468,000.

Therefore, there are 468,000 different license plates possible if repetition of numbers and letters is not permitted.

To find the number of different license plates possible, we need to determine the number of choices available for each position on the license plate and multiply them together.

Step 1: Number of choices for the first digit
Since repetition is not permitted, there are 10 choices (0-9) for the first digit.

Step 2: Number of choices for the second digit
Since repetition is not permitted, there are 9 choices (excluding the digit already chosen for the first digit) for the second digit.

Step 3: Number of choices for the third digit
Again, since repetition is not permitted, there are 8 choices for the third digit.

Step 4: Number of choices for the first letter
Since repetition is not permitted, there are 26 choices (A-Z) for the first letter.

Step 5: Number of choices for the second letter
Since repetition is not permitted, there are 25 choices (excluding the letter already chosen for the first letter) for the second letter.

To find the total number of different license plates, we multiply the number of choices for each position:

Total number of different license plates = (number of choices in step 1) × (number of choices in step 2) × (number of choices in step 3) × (number of choices in step 4) × (number of choices in step 5)

Total number of different license plates = 10 × 9 × 8 × 26 × 25

Calculating this expression gives us:

Total number of different license plates = 18,720,000

Therefore, there are 18,720,000 different license plates possible if repetition of numbers and letters is not permitted.