Repeat the preceding problem when the seating is random but subject to the constraint that the men and women alternate.
Preceding problem
A total of 2n people, consisting of n married couples, are randomly seated (all possible orderings being equally likely) at a round table. Let Ci denote the event that the members of couple i are seated next to each other, i = 1, . . . , n.
(a) Find P(Ci).
(b) For j ≠ i, find P(Cj|Ci).
(c) Approximate the probability, for n large, that there are no married couples who are seated next to each other.