Two persons are selected at random from n persons seated in a row (n ≥ 3). The probability that the selected persons are not seated consecutively, is equal to

$\frac{n-2}{n}$

Total ways of selecting two persons

$={ }^n C_2$

$=\frac{n(n-1)}{2}$

Total ways of selecting two consecutively seated persons

$={ }^{n-1} C_1$

= (n - 1)

Thus, required probability

$=1-\frac{(n-1) 2}{n(n-1)}$

$=\frac{n-2}{n}$