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 women sit together and all men sit together?

Answer 1

Solution:

We are given that: there are four married couples. Thus there are four Men and four women.

We have to arrange themselves such that all women seat together and all Men seat together.

Thus there are two different ways in which Men seat together and women seat together. But among four Men, they can seat together in 4! Ways. Similarly among four women, they can be seat together in 4! ways.

Thus total number of ways in which Men seat together and women seat together are

= 2 × 4! ×4!

= 2 × 4×3×2×1 × 4×3×2×1

=1152 ways.