(a) A football club has \(30\) players. In how many different ways can a captain and a vice-captain be selected at random from these players?

(b) A team of \(11\) teachers is to be chosen from \(2\) mathematics teachers, \(5\) computing teachers and \(9\) science teachers. Find the number of different teams that can be chosen if

(i) the team must have exactly \(1\) mathematics teacher,

(ii) the team must have exactly \(1\) mathematics teacher and at least \(4\) computing teachers.