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?

P.S. The answer is not 1440

Keihaku Sep 23, 2023

#3**0 **

There are 5 vowels: a, e, i, o, and u. There are 4 possible first digits: 1, 2, 4, and 6. For each of the three letters, there are 23 possible letters that can be used (since no letter can be repeated). For each of the three digits, there are 9 possible digits that can be used (since no digit can be repeated).

Therefore, the total number of possible license plates is 5 * 4 * 23 * 23 * 23 * 9 * 9 * 9 = 3000.

bingboy Oct 3, 2023