2007 AIME II Problem 1

A mathematical organization is producing a set of commemorative license plates.
Each plate contains a sequence of five characters chosen from the four letters in AIME and the four digits in 2007.
No character may appear in a sequence more times than it appears among the four letters in AIME or the four digits in 2007.
A set of plates in which each possible sequence appears exactly once contains N license plates. Find \frac{N}{10}.