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A group of 12 people who have never met are in a classroom. How many

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Math Expert
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A group of 12 people who have never met are in a classroom. How many  [#permalink]

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New post 03 Jan 2019, 09:34
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

73% (00:59) correct 28% (01:33) wrong based on 54 sessions

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Re: A group of 12 people who have never met are in a classroom. How many  [#permalink]

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New post 03 Jan 2019, 09:38
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Top Contributor
Bunuel wrote:
A group of 12 people who have never met are in a classroom. How many handshakes are exchanged if each pair shakes hands exactly once?

(A) 12
(B) 22
(C) 66
(D) 132
(E) 244


Here's an approach that doesn't require any counting techniques:

Since a person cannot shake hands with himself/herself, each person shakes hands with exactly 11 other people
So, we have 12 people and each experiences 11 handshakes for a TOTAL of 132handshakes [since (12)(11) = 132]

IMPORTANT: at this point, we need to recognize that every handshake has been counted TWICE. For example, if Person A and Person B shake hands, then Person A counts it as a handshake, AND Person B also counts it as a handshake. Of course only one handshake occurred.

To account for the DUPLICATION, we'll divide 132 by 2 to get 66

Answer: C

Cheers,
Brent
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Re: A group of 12 people who have never met are in a classroom. How many  [#permalink]

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New post 03 Jan 2019, 09:49
1
since each person will shake hands with the other person
so total handshakes = 12*11
however we have counted twice as only handshake is with other person
hence divide by 2
so (12*11)/2
general formula
n*(n-1)/2
=66
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Re: A group of 12 people who have never met are in a classroom. How many  [#permalink]

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New post 06 Jan 2019, 04:45
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Bunuel wrote:
A group of 12 people who have never met are in a classroom. How many handshakes are exchanged if each pair shakes hands exactly once?

(A) 12
(B) 22
(C) 66
(D) 132
(E) 244



12c2;

12!/10!*2!
= 66

IMO C
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Re: A group of 12 people who have never met are in a classroom. How many   [#permalink] 06 Jan 2019, 04:45
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