(a) Jess wants to arrange \(9\) different books on a shelf. There are \(4\) mathematics books, \(3\) physics books and \(2\) chemistry books. Find the number of different possible arrangements of the books if

(i) there are no restrictions,

(ii) a chemistry book is at each end of the shelf,

(iii) all the mathematics books are kept together and all the physics books are kept together.

(b) A quiz team of \(6\) children is to be chosen from a class of \(8\) boys and \(10\) girls. Find the number of ways of choosing the team if

(i) there are no restrictions,

(ii) there are more boys than girls in the team.