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
Answer & explanation
Correct answer: option 1
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
$=1-\frac{(n-1) 2}{n(n-1)}$
$=\frac{n-2}{n}$