Suppose `n ( >=3)` persons are sitting in a row. Two of them are selected at random. The probability that they are not together is (A) `1- 2/n` (B) `2/(n-1)` (C) `1- 1/n` (D) nonoe of these

Options

A. `1-(1)/(n)`
B. `1-(2)/(n)`
C. `(2)/(n+1)`
D. `(2)/(n)`

Answer

B

Explanation

The total number of ways of selecting 2 persons out of n persons sitting in a row is `.^(n)C_(2)`.
Number of ways in which two adjacent persons are selected from n persons sitting in a row =(n-1)
Hence, required probability `=(.^(n)C_(2)-(n-1))/(.^(n)C_(2))=1-(2)/(n)`