(a) Eight books are to be arranged on a shelf. There are 4 mathematics books, 3 geography books and 1 French book.

(i) Find the number of different arrangements if there are no restrictions.

(ii) Find the number of different arrangements if the mathematics books have to be kept together.

(iii) Find the number of different arrangements if the mathematics books have to be kept together and the geography books have to be kept together.

(b) A team of 6 players is to be chosen from 8 men and 4 women. Find the number of different ways this can be done if

(i) there are no restrictions,

(ii) there is at least one woman in the team.