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ps question 2

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by magical cook » Sat Oct 13, 2007 9:47 am
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?
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by Suyog » Sat Oct 13, 2007 10:44 pm
can you post the options?
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by samirpandeyit62 » Mon Oct 15, 2007 8:30 am
2 people can be selected out of 7 in 7c2 = 21 ways

now 4 people have exactly one friend i.e. they will constitute 2 combinations e.g AB CD (mutually 4 people with 1 friend each)

& 3 with two friends will make 3 combinations i.e EF FH HE

total =5 combinations

so probability that both are friends is 5/21

so P (both are not friends ) =1-5/21 = 16/21
Regards
Samir
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