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.

A total of 2n people, consisting of n married couples, are randomly seated (all posible 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 , find P(Cj l Ci). (c) Approximate the probability, for n large, that there are no married couples who are seated next to each other.

Solution

Prob that married couples together =

Prob that married couples not together= 1-

As n becomes very large the second term has sdenominator increasing faster than the numerator

Hence prob =1-0 =1