Question

Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if all the women sit together and all the men sit together

Answer 1

1152 ways

Explanation:

There are 4 married coupes i.e. four women and four men.

Let us treat four women as one unit together and 4 men as one unit together.

We have 2 units which can be arrangedi in 2!= 2 ways

Among 4 women they can arrnage themselves in 4! = 24 ways

Similarly 4 men can sit in 4! ways together

Hence total number of ways

they can arrange themselves if all the women sit together and all the men sit together

= No of ways 2 units arranged * no of ways men arranged * no of ways women arranged

=2*24*24

= 1152