Math Problem (Level 2) : Arrangement of numbers and alphabets (II10)

Based on the following [Rule 1] and [Rule 2], three kinds of number or alphabet are lined up in a row out of ten kinds of numbers from zero to nine and several kinds of alphabet.

[Rule 1]
Same number and alphabet may be used repeatedly.

[Rule 2]
It is not permitted that there are numbers only or alphabet only among three pieces.

Answer the following questions.

(1) When the alphabet is three kinds, A, B, and C, find all numbers of way for lining up.

(2) When the ways of lining up are 5000 or more kinds, find the fewest number of the kinds of the alphabet.

Answer

(1) 1170 ways
(2) 9