If n people are seated in a random manner in a row containing 2n seats, what is the probability that no two people will occupy adjacent seats? 10. a box contains 24 light bulbs, o

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 :

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