Last visit was: 06 Jun 2024, 03:54 It is currently 06 Jun 2024, 03:54
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Each of the 6 companies sends 3 people to a conference.

User avatar
gamjatang
Director
Director
Joined: 14 Sep 2005
Posts: 525
Own Kudos [?]: 1213 [0]
Given Kudos: 0
Location: South Korea
Send PM
Each of the 6 companies sends 3 people to a conference. [#permalink] Each of the 6 companies sends 3 people to a conference.   24 Nov 2005, 05:23
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (06:12) wrong based on 1 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
Each of the 6 companies sends 3 people to a conference.

Two people shakes hands.

What is the number of cases in which no two people from one same company shake hands?



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
BG
Senior Manager
Senior Manager
Joined: 13 Nov 2003
Posts: 356
Own Kudos [?]: 178 [0]
Given Kudos: 0
Location: BULGARIA
Concentration: INSURANCE, RISK MANAGEMENT
 Q49  V38
Send PM
Re: Each of the 6 companies sends 3 people to a conference. [#permalink] Each of the 6 companies sends 3 people to a conference.   24 Nov 2005, 10:25
18 people can shake hands in (18x17)/2=153 ways> When people in each team shake hands with each other (3x2)/2=3 handshakes per team or 18 for the six companies. Then 153-18=135
User avatar
christoph
Director
Director
Joined: 30 Sep 2004
Posts: 687
Own Kudos [?]: 1458 [0]
Given Kudos: 0
Location: Germany
Send PM
Re: Each of the 6 companies sends 3 people to a conference. [#permalink] Each of the 6 companies sends 3 people to a conference.   24 Nov 2005, 13:51
total number of handshakes is 18c2=153. total number of handshakes of 2 ppl in the same company is 3c2*6=18.153-18=135 !
User avatar
gamjatang
Director
Director
Joined: 14 Sep 2005
Posts: 525
Own Kudos [?]: 1213 [0]
Given Kudos: 0
Location: South Korea
Send PM
Re: Each of the 6 companies sends 3 people to a conference. [#permalink] Each of the 6 companies sends 3 people to a conference.   24 Nov 2005, 17:37
Good job !

The OA is 135.
User avatar
rianah100
Manager
Manager
Joined: 30 Aug 2005
Posts: 138
Own Kudos [?]: 19 [0]
Given Kudos: 0
Send PM
Re: Each of the 6 companies sends 3 people to a conference. [#permalink] Each of the 6 companies sends 3 people to a conference.   29 Nov 2005, 06:50
How about this?
You can select two groups out of 6 in 6C2 ways. within each groups, you can select one person in 3 ways.

So, 6C2*3*3= 135
User avatar
rianah100
Manager
Manager
Joined: 30 Aug 2005
Posts: 138
Own Kudos [?]: 19 [0]
Given Kudos: 0
Send PM
Re: Each of the 6 companies sends 3 people to a conference. [#permalink] Each of the 6 companies sends 3 people to a conference.   05 Dec 2005, 06:58
Why can't this be-
Select one group out of 6 in 6C1 ways, select one person out of 3 in 3 ways

Then select another group in 5C1 ways, select one person out of 3 in 3 ways

so, combinatons = 6*3*5*3=270

What am I missing?
User avatar
gamjatang
Director
Director
Joined: 14 Sep 2005
Posts: 525
Own Kudos [?]: 1213 [0]
Given Kudos: 0
Location: South Korea
Send PM
Re: Each of the 6 companies sends 3 people to a conference. [#permalink] Each of the 6 companies sends 3 people to a conference.   05 Dec 2005, 07:10
rianah100 wrote:
Why can't this be-
Select one group out of 6 in 6C1 ways, select one person out of 3 in 3 ways

Then select another group in 5C1 ways, select one person out of 3 in 3 ways

so, combinatons = 6*3*5*3=270

What am I missing?


You double counted the handshakes.

Suppose there are 6 groups - A, B, C, D, E, and F.

There are 3 members in group A, and they are A1, A2, and A3.
There are 3 members in group B, and they are B1, B2, and B3.

First, you pick group A, and pick person A1.
Then you pick group B, and pick person B1.

Again,
first, you pick group B, and pick person B1.
then you pick group A, and pick person A1.

The above two cases have to be counted as one.

Therefore, you have to divide your result by 2.
User avatar
automan
Senior Manager
Senior Manager
Joined: 09 Jul 2005
Posts: 320
Own Kudos [?]: 145 [0]
Given Kudos: 0
Send PM
Re: Each of the 6 companies sends 3 people to a conference. [#permalink] Each of the 6 companies sends 3 people to a conference.   05 Dec 2005, 10:35
When two different groups meet each other there are 9 handshakes. Thefeore the total number of handhakes will be:

9*5 + 9*4 + 9*3 + 9*2 + 9 =135
User avatar
krisrini
Manager
Manager
Joined: 15 Apr 2005
Posts: 159
Own Kudos [?]: 32 [0]
Given Kudos: 0
Location: India, Chennai
Send PM
Re: Each of the 6 companies sends 3 people to a conference. [#permalink] Each of the 6 companies sends 3 people to a conference.   06 Dec 2005, 01:42
Total no of people = 18
Total no of handshakes = 18C2
Total no of handshakes within the same company = 3C1, so for 6 companies it is 6*3C1= 18
18C2-18
= 17*18/2 - 18
= 18*(17/2-1)
= 9 *(15) = 135



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: Each of the 6 companies sends 3 people to a conference. [#permalink]
06 Dec 2005, 01:42
Moderators:
Bunuel
Math Expert
93575 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3131 posts