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Combinations - hand shake

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by crackgmat007 » Fri May 08, 2009 9:39 am
In a meeting of 3 representatives from each of 6 different companies, each person shook hands
with every person not from his or her own company. If the representatives did not shake hands
with people from their own company, how many handshakes took place?
A. 45
B. 135
C. 144
D. 270
E. 288

Pls explain the concept. Tx
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by scoobydooby » Fri May 08, 2009 10:07 am
we need to choose 2 people for one handshake.
total number of people in the meeting: 6*3=18
total handshakes that can happen among 18 people, (choosing 2 at a time for one handshake) : 18C2=153 handshakes.

the 3 representatives of one country do not shake hands with each other
=> handshakes that can happen among reps of one country: 3C2=3

there are 6 such countries, so 6*3=18 handshakes are not allowed.

allowed handshakes: 153-18=135

hence, B
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by vitaly » Fri May 08, 2009 1:15 pm
6 (from each of the companies) * 3 (each of the representatives) * 5 (rest of the companies) * 3 (each from the rest of the companies) / 2 (because we counted same handshake twice) = 135
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Re: Combinations - hand shake

by Brent@GMATPrepNow » Tue Jul 06, 2021 6:06 am
crackgmat007 wrote: ↑
Fri May 08, 2009 9:39 am
 In a meeting of 3 representatives from each of 6 different companies, each person shook hands
with every person not from his or her own company. If the representatives did not shake hands
with people from their own company, how many handshakes took place?
A. 45
B. 135
C. 144
D. 270
E. 288

Pls explain the concept. Tx
Let's focus on 1 person, call him Ted from company A.
Ted will shake hands with a total of 15 people (all 3 people who are in the other 5 companies).
Likewise, Ann from Company B will also shake hands with 15 people.
And so on....

In fact, all 18 people will shake hands with 15 others.

So, it SEEMS like the TOTAL number of handshakes = (18)(15)
HOWEVER, we need to keep in mind that we have counted each handshake TWICE.
That is, if Ted shakes hands with Ann, then we have counted that handshake once in Ted's 15 handshakes, AND once in Ann's 15 handshakes.
And so on...

To account for this DUPLICATION, we must divide (18)(15) by 2.
So, the TOTAL # of handshakes = (18)(15)/2 = 135 = B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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