The “problème des ménages” consists of finding the number of ways of seating $n$ married couples at a circular table, in such a way that men and women alternate and that no couple sits together. Here, the (more general) quantity of interest is the distribution of $W$, the number of couples seated together, if a random alternate seating plan is used. A new proof of the exact distribution of $W$ is given, and it is also shown that the $Bi(2n,1/n)$ distribution is an approximation accurate to order $n\sp{-2}$ in total variation.
Reviewer: A.D.Barbour (Zürich)