Question

There are n persons sitting in a row. Two of them are

selected at random. The probability that two selected

persons are not together is

• A. 2/n
• B. 1-2/n
• C. $\frac { \mathrm { n } ( \mathrm { n } - 1 ) } { ( \mathrm { n } + 1 ) ( \mathrm { n } + 2 ) }$
• D. None of these

Answer 1

Answer: (B)

1-2/n

Answer 2

The total number of ways of selecting two persons out of n is ${ } ^ { \mathrm { n } } \mathrm { C } _ { 2 } = \frac { \mathrm { n } ( \mathrm { n } - 1 ) } { 2 }$

The number of ways in which two selected persons are together is $( n - 1 )$ . So, the probability that the selected persons are together is

Hence, required probability $= 1 - \frac { 2 } { n }$ .