1.5: Book arrangements and sports team selection

0606/12/M/J/19 — Question 6 · 10 marks

(a)(i)
Eight books are to be arranged on a shelf. There are 4 mathematics books, 3 geography books and 1 French book. Find the number of different arrangements of the books if there are no restrictions.
[1]
(a)(ii)
Eight books are to be arranged on a shelf. There are 4 mathematics books, 3 geography books and 1 French book. Find the number of different arrangements if the mathematics books have to be kept together.
[3]
(a)(iii)
Eight books are to be arranged on a shelf. There are 4 mathematics books, 3 geography books and 1 French book. Find the number of different arrangements if the mathematics books have to be kept together and the geography books have to be kept together.
[3]
(b)(i)
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 there are no restrictions.
[1]
(b)(ii)
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 there is at least one woman in the team.
[2]