(a) A 6-digit number is formed using each of the digits \(1\), \(3\), \(5\), \(6\), \(8\), and \(9\) once and only once. Find the number of different 6-digit numbers that can be formed if

(i) there are no restrictions,

(ii) the number is even,

(iii) the number is even and greater than \(300000\).

(b) Ruby has \(15\) friends. She decides to invite \(8\) of them to a party. Find the number of ways in which she can do this if

(i) there are no restrictions,

(ii) two of the \(15\) friends are twins who must not be separated.