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

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Director
Joined: 14 Sep 2005
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Each of the 6 companies sends 3 people to a conference.  [#permalink]  24 Nov 2005, 04:23
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0% (00:00) correct 100% (06:12) wrong based on 1 sessions
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?
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Director
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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
VP
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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 !
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Director
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Good job !

The OA is 135.
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Manager
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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
Manager
Joined: 30 Aug 2005
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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?
Director
Joined: 14 Sep 2005
Posts: 994
Location: South Korea
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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.
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Director
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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
Senior Manager
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Re: PS - Shaking hands [#permalink]  06 Dec 2005, 00:42
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
Re: PS - Shaking hands   [#permalink] 06 Dec 2005, 00:42
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