srivathsan wrote:If three letters are put in three envelope with three diff. addresses, what is the probability that no addressee receives the correct letter?
a.1/6
b.1/4
c.1/3
d.1/2
e.2/3
Given the small number of possible outcomes here, we should also consider simply listing the possibilities.
Aside: Students often discount listing as a viable strategy because it doesn't seem very "mathematical," but we should always keep in mind that
our goal here is not to impress our former math teachers; our goal is to maximize our GMAT score.
Okay, let's list the outcomes systematically. I'll list each outcome as a 3-element set consisting of a, b and c. The first element indicates the letter that Person A receives, the second element indicates the letter that Person B receives, and the third element indicates the letter that Person C receives.
So, for example, the outcome {b, a, c} indicates Person A getting letter b, Person B getting letter a, and Person C getting letter c. So, here one of the people (Person C) received the letter destined for him/her.
Okay, now for the outcomes
1. {a, b, c}
2. {a, c, b}
3. {b, a, c}
4.
{b, c, a}
5.
{c, a, b}
6. {c, b, a}
Of the 6 possible outcomes, only
2 of them are such that no person receives the correct letter.
So, P(no one gets the correct letter) =
2/6
= 1/3
=
C
Cheers,
Brent
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