Question

A group of 12 people consists of 6 married couple.
(i) The group in a line
(a) Find the number of different possible orders.
(b) Find the number of different possible orders in which each man stand next to his wife.
(ii) The group stands in a circle.
(a) Find the number of different possible arrangement
(b) Find the number of different possible arrangements if men and women alternate.
(c) Find the number of different possible arrangements if each man stand to his wife and men and women alternate.

Answer 1

(i) (a) 12!
(i) (b) 6!(2!)^6=46080

(ii) a) 11!
(ii) b) HELP!
(ii) c) HELP!

Answer 2

What does it means by alternate?

Answer 3

alternate means :
ex. w-m-w-m-w-m-w-m-w-m-w-m

Answer 4

but arrangements in circle not row

Answer 5

so, the number of different possible arrangements if men and women alternate is
.
= 2*(5!)^2 = 2*(120)^2 = 2*(14400) = 28800 ways