Question

Fifteen people sit around a circular table. What are odds against two particular people sitting together?

Answer 1

The number of ways in which 15 people can be seated in a round table is, $(n-1)!=(15-1)!=14!ways$

and the number of ways if 2 people out of 15 sit together is, $(n-2)!*2=(15-2)!*2=13!*2ways$

To determine the odds, we first find the probability of 2 particular persons sitting together and it is given as,

13!*2/14!=1/7

Therefore, the odds against 2 particular persons sitting together is, 6:1