Repeat the preceding problem when the seating is random but subject to the const

Question

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.

Explanation / Answer

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

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