Question

n (≥ 3) persons are sitting in a row. Two of them are selected. Write the probability that they are together.

Answer 1

It is given that n (≥ 3) persons are seated in a row and two persons are selected.
∴ Total number of elementary event = n(S) = ⁿC₂
Let E be the event associated with the experiment that two persons are together.
∴ n(E) = ^{n -1}C_¹
Thus, required probability = P(E) = $\frac{n\left(E\right)}{n\left(S\right)}$
=$\frac{{}^{n-1}C_1}{{}^{n}C_2}$
=$\frac{\left(n-1\right)}{{\displaystyle \frac{n\left(n-1\right)}{2}}}=\frac{2\left(n-1\right)}{n\left(n-1\right)}=\frac{2}{n}$