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

1152 ways

Step-by-step 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