Question

Ajay write letters to his five friends and addresses the corresponding. The number of ways can the letters be placed in the envelopes so that atleast two of them are in the wrong envelopes is

• A. 120
• B. 125
• C. 119
• D. 130

Answer 1

The correct option is C 119

For this we know that derangement is an arrangement with all objects and of their proper place and particle derangement have some of the total objects derangement .

Fortunately this particular q can be solved w/o going into details about derangement from denoting a total derangement of $n$ objects by $D_n$,

$D_o$ is obviously $1$(i.e all are in their proper place $0$. $D_1$ is 0 because we just can't have $1$ object out of a set of n out of its place.

Thus, $P$(at least $2$ deranged)=Total arrangement. $D_0-D_1$

$=5!-1-0=119$

Hence,

Option $C$ is correct answer.