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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
Posts: 115
Followers: 1

Kudos [?]: 84 [0], given: 10

If 10 persons meet at a reunion and each person shakes hands [#permalink]  09 Mar 2011, 14:12
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Difficulty:

15% (low)

Question Stats:

72% (01:25) correct 28% (00:29) wrong based on 193 sessions
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
Math Expert
Joined: 02 Sep 2009
Posts: 27526
Followers: 4324

Kudos [?]: 42532 [0], given: 6038

Re: . If 10 persons meet at a reunion and each person shakes han [#permalink]  09 Mar 2011, 14:20
Expert's post
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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GMAT 1: 470 Q37 V18
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Followers: 0

Kudos [?]: 11 [1] , given: 57

Re: If 10 persons meet at a reunion and each person shakes hands [#permalink]  29 Apr 2014, 11:17
1
KUDOS
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] 29 Apr 2014, 11:17
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# If 10 persons meet at a reunion and each person shakes hands

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