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

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Kudos [?]: 40 [0], given: 10

If 10 persons meet at a reunion and each person shakes hands [#permalink] New post 09 Mar 2011, 14:12
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

70% (01:27) correct 30% (00:30) wrong based on 159 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
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Kudos [?]: 28977 [0], given: 2874

Re: . If 10 persons meet at a reunion and each person shakes han [#permalink] New post 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.

Answer: D.
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Kudos [?]: 7 [1] , given: 46

Re: If 10 persons meet at a reunion and each person shakes hands [#permalink] New post 29 Apr 2014, 11:17
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This post received
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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.

Hence answer D.
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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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