number of handshakes

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aditya.j: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Sun Jul 17, 2011 2:58 am; Thanked: 1 times

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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Source: Beat The GMAT — Problem Solving | Sun Dec 18, 2011 6:04 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

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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LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members; Thanked: 56 times; GMAT Score:690

by LalaB » Sun Dec 18, 2011 8:32 am

12*11/2=66

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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)

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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ankush123251: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Thu Feb 17, 2011 1:36 amFollowed by: 2 members; Thanked: 8 times

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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