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# In a room filled with 7 people, 4 people have exactly 1

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Manager
Joined: 29 Jul 2007
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In a room filled with 7 people, 4 people have exactly 1 [#permalink]  18 Nov 2007, 11:48
In a room filled with 7 people, 4 people have exactly 1 friend in the room and 3 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if John is Peter's friend, Peter is John's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?

a)5/21
b)3/7
c)4/7
d)5/7
e)16/21
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Kudos [?]: 2143 [0], given: 359

[#permalink]  18 Nov 2007, 12:18
Expert's post
e

p=1-q=1-(4*1/6+3*2/6)/7=1-5/21=16/21
Manager
Joined: 26 Sep 2007
Posts: 65
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Kudos [?]: 11 [0], given: 5

[#permalink]  18 Nov 2007, 17:54
walker wrote:
e

p=1-q=1-(4*1/6+3*2/6)/7=1-5/21=16/21

Walker, could you please explain in more detail?
VP
Joined: 08 Jun 2005
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[#permalink]  18 Nov 2007, 18:18
4/7)*(1/6) = 4/42 (choosing a person that has only 1 friend out of seven and choosing his friend out of 6)

(3/7)*(2/6) = 6/42 (choosing a person that has 2 friends out of seven and choosing his friend , he has two, out of 6)

4/42+6/42 = 10/42 = 5/21

but we need 1-(5/21) = 16/21

the answer is (E)

Manager
Joined: 26 Sep 2007
Posts: 65
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Kudos [?]: 11 [0], given: 5

[#permalink]  18 Nov 2007, 18:47
KillerSquirrel wrote:
4/7)*(1/6) = 4/42 (choosing a person that has only 1 friend out of seven and choosing his friend out of 6)

(3/7)*(2/6) = 6/42 (choosing a person that has 2 friends out of seven and choosing his friend , he has two, out of 6)

4/42+6/42 = 10/42 = 5/21

but we need 1-(5/21) = 16/21

the answer is (E)

KillerSquirrel, thanks for the explanation.
Manager
Joined: 03 Sep 2006
Posts: 233
Followers: 1

Kudos [?]: 5 [0], given: 0

[#permalink]  18 Nov 2007, 19:23
KillerSquirrel, thanks a lot - I was lost in this Q ...
[#permalink] 18 Nov 2007, 19:23
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# In a room filled with 7 people, 4 people have exactly 1

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