There are 3 letters and 3 addressed envelopes corresponding to them. The number of ways in which the letters be placed in the envelopes so that no letter is in the right envelope is

No of letters=n=3

No of envelopes=3

No of ways of placing the 3 letters in 3 envelopes. So that no letter is in right place

$$\begin{gathered} =\mathrm{n}! \left(1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3! \\ }+ ....\right) \\ =3! \left(\frac{1}{2!}-\frac{1}{3!}\right)=6\left(\frac{1}{2}-\frac{1}{6}\right) \\ =3-1=2 \end{gathered}$$

option (4) is correct.