To find the probability that no two people will occupy adjacent
seats, consider that n people are seated in a random manner in a row containing
2n seats. Using counting rule for combinations the total number of ways to
select n seats of 2n seats is N=(2n/n).
Now consider an event M that
all two people occupy adjacent seats. This can be done by occupying all odd
seats so that the even seats are left empty. This arrangement leaves the last
2nth seat empty. Even if one occupies that seat the condition of the event will
not break. So, we have (n + 1) seats available for the n people to seat so that
no two people occupy adjacent seats. N(M) = (n+1). Thus, the probability that
no two people will occupy adjacent seats in a row of 2n seats can be computed
as shown :
