How many ways are there to seat `n` married couples `(ngeq3)` around a table such that men and women alternate and each women is not adjacent to her husband.

Explanation

Number of ways of seating n couples in an alternating manner, i.e., one women one man and so on..=(n-1)!n!
Number of ways couples can be seated together always is `(n-1)!xx2!`
`therefore` Required number of ways =n!(n-1)!-2(n-1)!