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Delegations

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VP
Joined: 06 Feb 2007
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23 Mar 2007, 12:44
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Please provide your explanations. Does anybody know a book that explains combinatorics/probability concepts well?

Six three-representative delegations attend an international conference. The representatives shake hands when they are introduced to one another. How many handshakes are possible if each delegate shakes hands only once with every other attendant except with those of his/her delegation?

A) 36
B) 72
C) 90
D) 135
E) 388
Manager
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23 Mar 2007, 15:52
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D) 135

Lets say we got:
AAA BBB CCC DDD EEE FFF

1) For A's: 3*15=45 hand shakes
2) For B's: 3*12=36 hand shakes (excluding hand shake with A bcs it ocurred in 1)
3) For C's: 3*9=27 hand shakes (excluding hand shake with A and B bcs it ocurredin 1 and 2)
4) For D's: 3*6=18 hand shakes (excluding hand shake with A, B and C bcs it ocurred in 1, 2 and 3).
5) For E's: 3*3=9 hand shakes

=45+36+27+18+9=135
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Director
Joined: 14 Jan 2007
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24 Mar 2007, 08:57
I agree with X&Y 's explanation.
Manager
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24 Mar 2007, 11:20
yes I also believe X&Y is correct, and therefore he may want to double check his answer.
VP
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24 Mar 2007, 13:33
The OA is D indeed.
X&Y, great job!
Director
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24 Mar 2007, 22:39
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another way to solve it ..

total 18 folks ..

so total handshakes possible = 18c2 = 153

they dont shake hands within the group ..

within the group = 3c2 = 3 handshakes , hence for 6 groups = 18 handshakes

so, req number = 153 - 18 = 135
GMAT Club Legend
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22 Dec 2016, 10:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Delegations   [#permalink] 22 Dec 2016, 10:53
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Delegations

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