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 \(\frac{N}{10}\).

(第二十五届AIME2 2007 第1题)