Question

In how many ways $n$ married couples can be arranged around a table so that men and women are alternate and each woman is not adjacent to her husband?

• A. $(n-1)!(n!-2!)$
• B. $n!(n!-2!)$
• C. $(n!-2!)$
• D. $(n-1)!n!$

Answer 1

The correct option is A

$(n-1)!(n!-2!)$

Number of alternate arrangements $=(n-1)!n!$

Number of ways in which couples are seated together $=(n-1)!2!$

$\Rightarrow$ Number of ways in which men and women are alternate and each woman is not adjacent to her husband$=(n-1)!n!-(n-1)!2!$

$=(n-1)!(n!-2!)$