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

I will assume that two of the same letter (such as BB) and two or three of the same digit (such as 211 or 111) can appear on a single license plate. What I assume is meant is that no two license plates can be the same.

In that case, the answer is (26^2)*1000
= 676,000

If not, then the answer is
26*25 * 10*9*8 = 468,000

find n if p(n,4)=42p(n,2)

Well, isn't this a license to thrill? Let's do some math that doesn't require a driving test!

For the first letter of the license plate, you have 26 options (from A to Z).

Once the first letter is chosen, you have 25 options left for the second letter.

For the first digit, you have 10 options (from 0 to 9).

After the first digit is chosen, you have 9 options left for the second digit.

Finally, for the third and last digit, you have 8 options left.

To determine the total number of license plates possible, you need to multiply all these options together:

26 options × 25 options × 10 options × 9 options × 8 options = 468,000 possible license plates.

So, my friend, there you have it! With no repetition allowed, you could have 468,000 different license plates to choose from. That's more license plates than there are clowns at a circus!

To determine the number of different license plates possible without repetition of letters and numbers, we will calculate the number of possibilities for each component.

1. There are 26 letters in the English alphabet. Since repetition is not allowed, the first letter on the license plate can be chosen from any of the 26 options.
Once the first letter is chosen, there are only 25 remaining letters to choose from for the second letter.

Total Number of Options for Letters = 26 * 25 = 650

2. There are 10 digits (0-9) to choose from for the three digits on the license plate. Since repetition is not allowed, the first digit could be chosen from any of the 10 options. After selecting the first digit, there would be 9 remaining options for the second digit, and 8 remaining options for the third digit.

Total Number of Options for Digits = 10 * 9 * 8 = 720

3. To calculate the total number of different license plates possible, we multiply the number of options for letters by the number of options for digits.

Total Number of Different License Plates = Total Number of Options for Letters * Total Number of Options for Digits
= 650 * 720
= 468,000

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

To determine the number of different license plates possible without repetition of letters and numbers, we need to consider the number of options for each part of the license plate.

1. Letters: There are 26 letters in the English alphabet (A to Z). Since repetition is not permitted, there are 26 options for the first letter and 25 options for the second letter (as it cannot be the same as the first letter). Therefore, there are a total of 26 * 25 = 650 options for the letters.

2. Digits: There are 10 digits (0 to 9) to choose from. Since repetition is not permitted, there are 10 options for the first digit, 9 options for the second digit, and 8 options for the third digit. Therefore, there are a total of 10 * 9 * 8 = 720 options for the digits.

To find the total number of different license plates possible, we multiply the number of options for each part:

Total number of different license plates = Number of options for letters * Number of options for digits
= 650 * 720
= 468,000

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