how many 4 character license plates are possible with 2 letters of the alphabet followed by 2 digits, it repetitions are allowed?

if repetitions are not allowed?

Assuming all 26 letters are used, there is a choice of 25 letters for the first character, 26 for the second, 10 for the third, and 9 for the fourth.

The total number is the product of the four numbers.

If repetitions are allowed, the choies are 26,26,10,10.

To determine the number of possible 4 character license plates with repetitions allowed, we need to consider the number of choices for each character.

In this case, there are 26 letters in the alphabet and 10 digits (0-9). Therefore, there are 26 choices for the first letter, 26 choices for the second letter, 10 choices for the first digit, and 10 choices for the second digit.

To calculate the total number of possible license plates, we multiply the number of choices together:

26 choices for the first letter x 26 choices for the second letter x 10 choices for the first digit x 10 choices for the second digit = 67,600 possible license plates.

Now let's consider the scenario where repetitions are not allowed.

For the first letter, there are 26 choices as before. However, for the second letter, since repetitions are not allowed, there are only 25 choices remaining (excluding the one already chosen for the first letter). Similarly, for the first digit, there are 10 choices, and for the second digit, since repetitions are not allowed, there are 9 choices remaining (excluding the one already chosen for the first digit).

To calculate the total number of possible license plates without repetitions, we multiply the number of choices together:

26 choices for the first letter x 25 choices for the second letter x 10 choices for the first digit x 9 choices for the second digit = 58,500 possible license plates without repetitions.