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Question

There are n different object 1, 2, 3, ... n distributed at random in n boxes A1,A2,A3,AN. Find the probability that two objects are placed in the boxes corresponding to their number.

A
1
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B
12
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C
13
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D
23
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Solution

The correct option is A 12
Let Ei be the event that ith object is placed in ithe box,
P(Ei)=1.(n1)n!=1n,i=1,2n.
Now the probability that two boxes contain right objects.P(EiEj)=1.(n2)!n!
and these two objects can be out of n objects in nC2ways.
So the probability that two objects are in right boxes.=nC2(n2)!n!=n!2!(n2)!.(n2)n!=12.

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