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Question

There are n persons sitting in a row. Two of them are selected at random. The probability that the two selected persons are not together, is

A
2n
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B
12n
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C
n(n1)(n+1)(n+2)
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D
None of these
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Solution

The correct option is B 12n
Total persons= n

Total number of wage to select two at a time = nC2
No. of ways to select two together person= n1

Probability of two together person,
= n1nC2
= n1n!/(n2)!2!

= (n1)(n2)!2n(n1)(n2)!

= 12n

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