Probability-how do you go about solving this problem

[fosterb09]

Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?

1) 1/24 2) 1/8 3) 1/4 4)1/3 5) 3/8

[fosterb09]

The question is from gmatprep 2.0

[jnelson0612]

Please see this thread in which this problem is discussed: post5773.html

[joindk]

HI, here is what I think:

One must go in correct: choose one = 4C1 = 4 ways
now you are left with 3 to put in wrong envelope ( making sure all three goes in wrong envelope)

number of ways of arranging them = 3!, but this contains when

all three goes in correct envelope = 1 way
two goes in correct envelop = same case as all thee goes in correct envelope. - discard

one goes in correct envelope = 3C1 = 3 ways (just select which one goes in correct envelope)

so, number of ways to put 3 letters in wring envelope= 3! - (1+3)
= 2
=> total ways to do the job = 4*2

total ways of putting 4 letters in 4 envelope = 4!

Probability = 8/4! = 1/3

[RonPurewal]

please post any further questions on the thread that jamie linked; this thread is now locked.

thanks.