A group of 2n individuals, consisting of n couples, are arranged at round table. How to find an upper bound for the probability that none of the couples seated next to each other?
as stated the problem doesn't make too much sense.
If I seat each member of a couple across from the other none will sit next to the other.
Thus the probability of none seated next to the other is 1.
any probability is less than or equal to 1 so this must be the upper bound.
Do you mean that people are seated at random and you want to know the probability of arrangements where no couples are seated next to one another?