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(C) The total number of ways to arrange $4$ letters in $4$ envelopes is $4! = 24$.The number of ways in which all letters go into their correct envelo

Vedclass · Accepted Answer

$\frac{23}{24}$

Vedclass · Answer

(C) The total number of ways to arrange $4$ letters in $4$ envelopes is $4! = 24$.The number of ways in which all letters go into their correct envelopes is $1$.The probability that all letters go into their correct envelopes is $P(	ext{correct}) = \frac{1}{4!} = \frac{1}{24}$.The probability that no letter goes into its correct envelope (a derangement) is $1 - P(	ext{correct})$.Therefore,the required probability is $1 - \frac{1}{24} = \frac{23}{24}$.

There are $4$ envelopes with addresses and $4$ corresponding letters. The probability that no letter goes into its correct envelope is:

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