Question 2103
A group of 12 people consists of 5 married couples, 1 single man and 1 single woman.
(a) The group stand in a line.
(i) (1 mark) Find the number of different possible orders.
(ii) (3 marks) Find the number of different possible orders in which each married man stands next to his wife.
(iii) (2 marks) Find the number of different possible orders if men and women alternate.
(iv) (3 marks) Find the number of different possible orders if each married man stands next to his wife and men and women alternate.
(b) The group stand in a circle.
(i) (1 mark) Find the number of different possible orders.
(ii) (3 marks) Find the number of different possible orders in which each married man stands next to his wife.
(iii) (2 marks) Find the number of different possible orders if men and women alternate.
(iv) (3 marks) Find the number of different possible orders if each married man stands next to his wife and men and women alternate.