.We need to find the probability that atleast one letter was put in the correct envelope.
The total number of ways of putting three letters in 3 envelopes = 3 x 2 x 1 = 6
The number of ways of putting all three letters in incorrect envelope is =2
Letter for X goes into envelope for Y and Letter for Y goes into envelope for Z, Letter for Z goes
into envelope for X
or Letter for X goes into envelope for Z and Letter for Y goes into envelope for X and Letter for Z goes into
envelope for Y ]
2 1
P(None of the letters is put in the right envelope) =
6 3
P(Atleast one letter is put in the right envelope)=
=
1 2
1 _ - P(None of the letters is put in the right envelope) 1
3 3