How many ways are there to set n – married couples $(n\ge 3)$around a table such that men and women alternative and each women is not adjacent to her husband.

Men = n

Women = n

$(n-1)!\times n!\Rightarrow$ Total number of ways men and women are sitting alternatively.

Number of ways husband and wife are sitting together

$\Rightarrow (n-1)!{}^2{C}_1$$\Rightarrow 2(n-1)!$

Number of ways men and women are sitting alternatively and husband and wife are not sitting together $\Rightarrow (n-1)!n!-2(n-1)!$