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

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

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New post 09 Mar 2011, 15:12
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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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New post 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 \(C^2_{10}=45\).

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

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New post 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.

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

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New post 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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New post 16 Sep 2015, 21:03
Expert's post
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] 16 Sep 2015, 21:03
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