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Delegations

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VP
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Delegations [#permalink] New post 23 Mar 2007, 11:44
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
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 [#permalink] New post 23 Mar 2007, 14:52
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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 [#permalink] New post 24 Mar 2007, 07:57
My answer is 135.
I agree with X&Y 's explanation.
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 [#permalink] New post 24 Mar 2007, 10:20
yes I also believe X&Y is correct, and therefore he may want to double check his answer.
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 [#permalink] New post 24 Mar 2007, 12:33
The OA is D indeed.
X&Y, great job!
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 [#permalink] New post 24 Mar 2007, 21:39
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 :)
  [#permalink] 24 Mar 2007, 21:39
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