N2017 H1 Q8 [Modified]

A code consists of \(6\) characters. The first \(3\) characters of the code consists of \(3\) digits chosen from \(\left\{ 1,\,\,2,\,\,3,\,\,4,\,\,5,\,\,6 \right\}\).

The last \(3\) characters of the code consists of \(3\) letters chosen from \(\left\{ A,\,\,B,\,\,C,\,\,D,\,\,E,\,\,F,\,\,G,\,\,H \right\}\).

1. How many codes can be formed if repetitions are not allowed?

Now suppose that repetitions are allowed. Find the number of codes that

2. contain the digit \(5\) exactly once and the letter \(H\) exactly twice.
3. have \(2\) as its first character or \(H\) as its sixth character, but not both.