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number of handshakes

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by aditya.j » Sun Dec 18, 2011 6:04 am
12 People meet in a party and each person shakes hand with every one else. What is the minimum number of handshakes ?


a)6

b)66

c)132

d)11!

e)12!
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by shankar.ashwin » Sun Dec 18, 2011 6:18 am
2 people are needed for a handshake. We have a total of 12 people.

Total number of handshakes is nothing but number of distinct ways of picking up 2 people from 12 (or) 12C2 = 66
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by LalaB » Sun Dec 18, 2011 8:32 am
12*11/2=66
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by Brent@GMATPrepNow » Sun Dec 18, 2011 1:44 pm
aditya.j wrote:12 People meet in a party and each person shakes hand with every one else. What is the minimum number of handshakes ?
a)6
b)66
c)132
d)11!
e)12!
Another approach (other than 12C2) is this:

If we ask each person, "How many people did you shake hands with?" we'll find that each person shook hands with 11 people, which gives us a total of 132 handshakes (since 12x11=132).

From here we need to recognize that each handshake has been counted twice. For example, if Person A and Person B shake hands, then Person A counts it as a handshake and Person B counts it as a handshake.

So, to account for the duplication, we'll divide 132 by 2 to get 66 (B)

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by ankush123251 » Mon Dec 19, 2011 3:25 am
@Brent-Isn't that the exactly reason why we have not done 12P2 and 12C2 because the order does not matter!!
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by Brent@GMATPrepNow » Tue Jan 31, 2012 8:41 am
ankush123251 wrote:@Brent-Isn't that the exactly reason why we have not done 12P2 and 12C2 because the order does not matter!!
Exactly.

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