A state creates license plates that each contain two letters followed by three digits. The first letter must be a vowel ( A, E, I, O, U ) and duplicate letters and digits are allowed. How many different license plates are possible?

Think about how many choices there are for each spot. Each choice is unaffected by the other choices.

5*26 * 10*10*10 = 130,000

To determine the number of different license plates that are possible, we need to consider the choices available for each position on the license plate.

The first position in the license plate can only be a vowel (A, E, I, O, or U), so there are 5 options for the first letter.

The second position in the license plate can be any letter (A, B, C, ..., Z), so there are 26 options for the second letter.

The third position in the license plate can be any digit (0, 1, 2, ..., 9), so there are 10 options for the first digit.

The fourth position in the license plate can also be any digit, giving us 10 options.

The fifth position in the license plate can be any digit as well, so there are 10 options.

Since each position on the license plate is independent and can have multiple choices, we can multiply the number of choices for each position to find the total number of possible license plates:

Total number of possible license plates = (number of choices for the first position) * (number of choices for the second position) * (number of choices for the third position) * (number of choices for the fourth position) * (number of choices for the fifth position)

Total number of possible license plates = 5 * 26 * 10 * 10 * 10

Calculating this gives us:

Total number of possible license plates = 13,000

Therefore, there are 13,000 different license plates possible.

To determine the number of different license plates that are possible, we need to consider the number of options for each character in the license plate.

1. The first letter must be a vowel. There are 5 vowels (A, E, I, O, U) that can be chosen for the first letter.

2. The second letter can be any letter of the alphabet, including duplicates. There are 26 letters in the English alphabet, so there are 26 options for the second letter.

3. The third, fourth, and fifth characters are digits. Since duplicate digits are allowed, each of these characters can be chosen from the 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).

Therefore, the total number of possible license plates can be calculated by multiplying the number of options for each character:

Number of possible license plates = Number of options for first letter * Number of options for second letter * Number of options for third digit * Number of options for fourth digit * Number of options for fifth digit

Number of possible license plates = 5 * 26 * 10 * 10 * 10 = 130,000

Therefore, there are a total of 130,000 different license plates that are possible based on the given criteria.