# Question: Repeat the preceding problem when the seating is random but

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.

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.

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