jmc

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: $$5\times 25\times 24=3000\text{ letter arrangements}$$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: $$4\times 9\times 8=288\text{ digit arrangements}$$Since the digits and letters can be arranged independently, the total number of license plates will be: $$3000\times 288=\boxed{864000}$$