On the ''problème des ménages'' (Q1160179)

The classical ``problème des ménages'' is altered in the following way: the \(n\) women take alternate seats and the \(n\) men choose the remaining seats at random such that all possible sitting arrangements are equally probable. The joint distribution of the random variables \(\xi_n\), the number of men sitting at the right-hand side of their wives, and \(\eta_n\), the number of men sitting at the left-hand side of their wives, is calculated for \(n= 1,2, \ldots\). One finds also a lot of references related to this subject.