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# If 10 persons meet at a reunion and each person shakes hands

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Manager
Joined: 10 Feb 2011
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If 10 persons meet at a reunion and each person shakes hands [#permalink]

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09 Mar 2011, 15:12
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Question Stats:

73% (01:26) correct 27% (00:32) wrong based on 319 sessions

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If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
(A) 10•9•8•7•6•5•4•3•2•1
(B) 10•10
(C) 10•9
(D) 45
(E) 36
[Reveal] Spoiler: OA
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Re: . If 10 persons meet at a reunion and each person shakes han [#permalink]

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09 Mar 2011, 15:20
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banksy wrote:
. If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
(A) 10•9•8•7•6•5•4•3•2•1
(B) 10•10
(C) 10•9
(D) 45
(E) 36

The total # of handshakes will be equal to the # of different pairs possible from these 10 people (one handshake per pair), so $$C^2_{10}=45$$.

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Re: If 10 persons meet at a reunion and each person shakes hands [#permalink]

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29 Apr 2014, 12:17
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We got #10 people who shake each other's hands once ==> a pair of 2

10!/8!2! = 10*9 / 2*1 = 45.

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Re: If 10 persons meet at a reunion and each person shakes hands [#permalink]

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16 Sep 2015, 16:56
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Re: If 10 persons meet at a reunion and each person shakes hands [#permalink]

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16 Sep 2015, 21:03
Handshakes are made in a pair of 2
Hence the total handshakes = total different different pairs

This can be found by 10C2= 10!/8!*2!

On solving , we get 45 (Option D)
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Re: If 10 persons meet at a reunion and each person shakes hands [#permalink]

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29 Mar 2017, 10:00
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: If 10 persons meet at a reunion and each person shakes hands   [#permalink] 29 Mar 2017, 10:00
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# If 10 persons meet at a reunion and each person shakes hands

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