Probability

The number of ways in which 4 letters can be placed in 4 envelopes is 4! = 24 ways

let L1, L2,L3 L4 be letters and E1,E2,E3,E4 be envelopes

Only one of the letter has to go into the correct envelope

Assume L1 goes to E1

We are left with L2,L3,L4 and E2,E3,E4.

Number of ways in which all the three letters go into different envelopes.

Total no of ways in which 3 letters can go to 3 envelopes = 3! = 6

No of ways in which all the 3 letters go in to correct envelopes = 1
Note ( If 2 letters go correct envelope the third one automatically does too)

No of ways in which one letter goes to correct envelopes = 3*1

No of ways in which none of the 3 letters go into correct envelopes = 6 -( 1 + 3) = 2

Any one of the four letters can go to correct envelope = 4*2 = 8

Probablityt = 8/24 = 1/3

Thanks
raama