A state creates license plates that each contain two letters followed by three digits. The first letter must be a vowel and duplicate letters and digits are allowed. How many different plates are possible?
5 vowels
26 letters
10 digits
# plates = 5*26*10^3
To find the number of different license plates possible, we need to consider the constraints given and calculate the total number of valid combinations.
1. The first letter must be a vowel: There are five vowels (A, E, I, O, U) that could be used as the first letter.
2. Duplicate letters are allowed: This means that for the second letter, any letter of the alphabet (including vowels) can be used.
3. Three digits are allowed: There are ten possible digits (0-9) that can be used for each of the three digit slots.
To calculate the total number of different license plates, we multiply the number of possibilities for each component together:
Number of possibilities for the first letter: 5 (since there are five vowels)
Number of possibilities for the second letter: 26 (since there are 26 letters in the English alphabet)
Number of possibilities for each digit slot: 10 (since there are ten digits)
Total number of different license plates = Number of possibilities for the first letter * Number of possibilities for the second letter * Number of possibilities for each digit slot
Therefore, the total number of different license plates possible can be calculated as:
5 * 26 * 10 * 10 * 10 = 130,000 plates
So, there are 130,000 different plates possible.