(D) The total number of ways to place $5$ letters in $5$ addressed envelopes is $5! = 120$. The number of ways in which all letters are placed in the

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(D) The total number of ways to place $5$ letters in $5$ addressed envelopes is $5! = 120$. The number of ways in which all letters are placed in the correct envelopes is $1$. Thus,the probability that all letters are placed correctly is $\frac{1}{120}$. The probability that at least one letter is placed in the wrongly addressed envelope is $1 - P(\text{all correct}) = 1 - \frac{1}{120} = \frac{119}{120}$.

Class 11 Mathematics Permutation and Combination Division into groups, Derangements

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If $5$ letters are to be placed in $5$ addressed envelopes,then the probability that at least one letter is placed in the wrongly addressed envelope is

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A
$\frac{1}{5}$
B
$\frac{1}{120}$
C
$\frac{4}{5}$
D
$\frac{119}{120}$

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Permutation and Combination

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Division into groups, Derangements

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If $5$ letters are to be placed in $5$ addressed envelopes,then the probability that at least one letter is placed in the wrongly addressed envelope is

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