Question

There are $m$ persons sitting in a row. two of them are selected at random. The probability that the two selected persons are not together is $1-\frac{2}{m}$. If true enter 1 else 0.

Answer 1

Total number of ways of selecting two persons out of $m$ is ${}^m{C}_2=\frac{m(m-1)}{2}$

Number of ways in which the two selected persons are together is $(m-1)$

Therefore, number of ways in which the two selected persons are not together is ${}^m{C}_2-(m-1)=\frac{(m-1)(m-2)}{2}$

Thus the probability of the required event is $\frac{(m-1)(m-2)/2}{m(m-1)/2}=\frac{m-2}{m}=1-\frac{2}{m}$