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# Manhattan Gmat Probability question

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Senior Manager
Joined: 14 Jul 2006
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Manhattan Gmat Probability question [#permalink]  31 Jul 2006, 23:34
Hi guys try this out

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. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
Senior Manager
Joined: 22 May 2006
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Location: Rancho Palos Verdes
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Total ways of selecting ppl. 7C2 = 21
Let
ABC(2friends)
CD(1friends)
DE(1friends)
ways of selecting those who are friends.
3C2+2C2+2C2 = 3+1+1 = 5

1-5/21 = 16/21
_________________

The only thing that matters is what you believe.

Senior Manager
Joined: 14 Jul 2006
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Man you guys are fast! yup that's the correct answer
SVP
Joined: 30 Mar 2006
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Let the friends be A B C D E F G
Probability of choosing 2 people = 7C2 = 21
Group of friends could be
AB CD EF FG EG

Hence there are 5 groups of friends.

We can choose friends from any of this group.
Hence Probability of choosing friends = 5/21

Probability of not choosing friends = 1 - 5/21 = 16/21
Senior Manager
Joined: 21 Jun 2006
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That's a great probability question!
Manager
Joined: 20 Mar 2006
Posts: 200
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Kudos [?]: 1 [0], given: 0

jaynayak wrote:
Let the friends be A B C D E F G
Probability of choosing 2 people = 7C2 = 21
Group of friends could be
AB CD EF FG EG

Hence there are 5 groups of friends.

We can choose friends from any of this group.
Hence Probability of choosing friends = 5/21

Probability of not choosing friends = 1 - 5/21 = 16/21

good approach

Heman
CEO
Joined: 20 Nov 2005
Posts: 2910
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
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Only possibility of group of friends is
12 - Both friends
34 - Both friends
456 - Each friend of the other

Total cases = 7C2 = 21

Cases when either 1 or 2 is selected as first person = 2 * 5 = 10
Cases when either 3 or 4 is selected as first person = 2 * 3 = 6

So Prob = 16/21
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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