Question

'n' person are seated on 'n' chairs at a round table. find the probability that two specified persons are sitting next to each other

Answer 1

Answer

The probability that two specified persons are sitting next to each other

          =2/(n-1)!                                                                                                                

Explanation

Let  'n' person are seated on 'n' chairs at a round table in (n-1)! ways

two specified persons are sitting next to each other, then there are n-1 entities,

So total number of ways these (n-1) entities are arranged in a circular table = (n-2)!

Also, the two person can be seated in 2! ways

Therefore, total number of ways these (n-1) entities are arranged in a circular table = 2! x (n-2)!= 2(n-2)!

The probability that two specified persons are sitting next to each other = 2(n-2)!/(n-1)!

                                                                                                                 =2/(n-1)!

Answer 2

probability = (n-1-1)!×2!/(n-1)! = 2/(n-1)