VeritasPrepKarishma wrote:

vardhanindaram wrote:

5 letters have to be put in 5 different envelopes numbered 1 through 5 such that each of the letters go into only 1 envelope.The letter is said to be put in correct position if for example letter 1 goes into envelope 1.Now what is the probability that all letters be put into wrong envelopes?

A. 1/3

B. 2/3

C. 11/120

D. 11/30

E. 76/120

Note that this question is not a GMAT type question. A GMAT type P&C question would be tricky, (perhaps fun!) but do-able in a minute or two. It would not depend on your knowledge of obscure formulas and would not require you to go through a ton of calculations.

A question which deals with 3 letters and 3 envelopes and asks you to say, find the number of ways in which at least 2 letters go in the correct envelope is far more GMAT friendly.

It would require you to realise that you cannot have exactly 2 letters going in the correct envelope so all you need to do is find the number of ways in which all 3 go in the correct envelope.

This post discusses the logic of putting letters into envelopes:

http://www.veritasprep.com/blog/2011/12 ... envelopes/Hi

VeritasPrepKarishma,

I am not able to solve this question by example approach; please help where am I making a mistake.

Let's say there are 5 letters--L1,L2,L3,L4,L5

and there are 5 envelopes- E1,E2,E3,E4,E5

L1 can be put incorrectly in 4 ways(E2,E3,E4,E5), let's say, it is put in E3

now, L3 can also be put incorrectly in 4 ways(E1,E2,E4,E5), lets say it is put in E2.

now, L2 can be put incorrectly in 3 ways(E1,E4,E5), let's say it is put in E5.

now, letters L5 and L4 are left and envelopes E1 and E4 are left, so these letters can be put in the incorrect envelope in just one way

so, total combinations are 4*4*3*1*1=48

p=48/120 (which is incorrect).

Am I solving it incorrectly?