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

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Joined: 10 Feb 2011
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Kudos [?]: 167 [0], given: 10

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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Difficulty:

5% (low)

Question Stats:

72% (01:26) correct 28% (00:34) wrong based on 251 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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Kudos [?]: 68448 [2] , given: 9805

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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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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Kudos [?]: 12 [1] , given: 57

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

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29 Apr 2014, 12:17
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]

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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
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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