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?
First, we can count the number of ways to arrange the letters.  There are $5$ choices for the first letter, since it must be a vowel.  This leaves $25$ possibilities for the second letter, since there are no repeats, and then $24$ possibilities for the third letter, for a total of: $$5\times25\times24=3000\text{ letter arrangements}$$Next, we can count the number of ways to arrange the digits.  There are $4$ possible choices for the first digit, corresponding to the four elements of the set $\{1,2,4,6\}$.  This leaves $9$ remaining choices for the next digit, and $8$ choices for the last digit, a total of: $$4\times9\times8=288\text{ digit arrangements}$$Since the digits and letters can be arranged independently, the total number of license plates will be: $$3000\times288=\boxed{864000}$$