There are 26 alphabets, and we want the first 3 to be different alphabets. So, the first three characters have the probability:
[tex]26*25*24[/tex]
Next, we want 5 different digits. There are 10 total digits (including 0), so that will look like:
[tex]10*9*8*7*6[/tex]
Combining those two statements, we get:
[tex]26*25*24*10*9*8*7*6[/tex]
Thus, your answer is 471744000.
