There are 5 letters and 5 addressed envelops. If the letters are put at random in the envelops, the probability that atleast one letter may be placed in wrongly addressed envelope is

There are 5 letters and 5 addressed envelops. The letters are put at random in the envelops

$n\left(S\right)=5!$

E=Event of arranging so that atleast one letter may be placed in wrongly addressed envelope is

$\mathrm{P}\left(\mathrm{Atleast} \mathrm{one} \mathrm{in} \mathrm{wrong}\right)=1-\mathrm{P}\left(\mathrm{All} \mathrm{letters} \mathrm{are} \mathrm{placed} \mathrm{correctly}\right)$

$\therefore P\left(E\right)=1-\frac{1}{120}=\frac{119}{120}$