GMAT Prep - Probability: Envelops and Letters

netigen

This is from GMATPrep,

John wrote 4 letters to four friends and then addressed four envelops, one each for each letter, Assuming all 4 addresses are different what is the probability that only one letter makes it to its envelop.

jscoligan · Posted: Mon May 12, 2008 11:04 am Post subject: Total Guess

Is the answer 27/256?

If not, what is?

netigen · Posted: Mon May 12, 2008 11:14 am Post subject: Re: Total Guess

I think the answer was 1/3

akshatsingh · Posted: Mon May 12, 2008 11:41 pm Post subject:

Four envelopes
[] [] [] []
y x x x

1/4 2/3 1/2 1/1

For the second one 2 wrong ones from 3 right ones can be picked
For the third one 1 wrong one from remaining 2 right ones can be picked
For the fourth one 1 wrong one only is left. so 1/1

there can be 4 different ways of attaining a y.
therefore, 4*(1/4)(2/3)(1/2)(1/1) = 1/3

I hope this is correct..