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Question: There are n letters and n addressed envelopes. The probability that all the letters are not kept in ...

There are n letters and n addressed envelopes. The probability that all the letters are not kept in the right envelope, is

A

1n!\frac { 1 } { n ! }

B

1−1n!1 - \frac { 1 } { n ! }

C

1−1n1 - \frac { 1 } { n }

D

None of these

Answer

1−1n!1 - \frac { 1 } { n ! }

Explanation

Solution

Required probability is 1−P1 - P (All letters in right envelope) =1−1n!= 1 - \frac { 1 } { n ! }

{As there are total number of n!n ! ways in which letters can take envelopes and just one way in which they have corresponding envelopes}.