Question

15 person among whom are aand b sit down at random at a round at a round table the probability that there are 4 persons

Answer 1

Number of ways you arrange 15 persons around a round table is 1/15 15! =14!.  

Now, consider the 4 people that would sit together as one person. That leaves us with 1/12 persons. The number of ways to swat 12 people around a round table is 1/12 12! = 11!.  

Finally, consider the 4! permutations among the 4 people that sit together, and you have the required probability as:

11! ×4! / 14!=4/91

Answer 2

Given:

15 persons

a and b sit at random position

To find:

The probability that there are 4 persons

Solution:

By permutation,

The number of ways 15 persons can be arranged around a round table is,

14 !  

As 4 people would always sit together,

The number of ways 12 persons can be arranged around a round table is,

11 !

The required probability,

Number of ways 11 people can be arranged * Number of people the 4 people can be arranged so that they always sit together / Number of ways 15 people can be arranget

11 ! * 4 ! / 14 !

4 / 91

Hence, the probability that there are 4 persons is 4 / 91