A \(6\)-character password is to be formed from the following characters.

Letters: \(A,\ B,\ C,\ D\)

Numbers: \(1,\ 2,\ 3,\ 4\)

Symbols: \(*,\ \#,\ \$,\ \pounds\)

No character may be used more than once in any password.

(a)(i) Find the number of different \(6\)-character passwords that can be formed.

(a)(ii) How many of these \(6\)-character passwords end with a symbol?

(b) Find the number of different \(6\)-character passwords that include all the symbols, but do not start or end with a symbol.