License plates in the newly established state of atlantis consist of three letters followed by three digits. the first letter must be a vowel (y is not considered a vowel), and no letter can be repeated. the first digit must be one of $\{1,2,4,6\}$, which corresponds to the location the license was issued. no digit may be repeated. how many possible license plates exist?

864000 license plates.

Step-by-step explanation:

The first letter has to be a vowel, so we have a,e,i,o,u=5 choices first.

The second letter could be anything except the first one, so we have 25 choices.

The third could be any letter except the first two, so we have 24 choices.

The first digit has to be 1, 2, 4, 6=4 choices.

The second digit has to be any one except the first so we have 9 choices.

The last digit has 8 choices for the reasons stated above.

We multiply it all together and have 864000 license plates.