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# If 10 people meet at a reunion and each person shake hands

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Manager
Joined: 12 Feb 2008
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If 10 people meet at a reunion and each person shake hands [#permalink]

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16 Jul 2008, 07:40
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If 10 people meet at a reunion and each person shake hands exactly once with each 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

thank you

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SVP
Joined: 30 Apr 2008
Posts: 1867

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Location: Oklahoma City
Schools: Hard Knocks
Re: PS probability or else? [#permalink]

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16 Jul 2008, 07:47
D) 45

If you number them #1 through #10 just to help identify them, then will be something like this

#10 - 9 hand shakes (the other 9 people)
#9 - 8 hand shakes (he doesn't need to reshake #10's hand)
#8 - 7 hand shakes (he doesn't need to reshake #10's and #9's hand)
...
#3 - 2 hand shakes (he doesn't need to reshake all the other's hands and #2 & #1 are the only ones he has not
#2 - 1 hand shake (he only had #1 left that he has not shaken hands with)

9+8+7+6+5+4+3+2+1 = 45

elmagnifico wrote:
If 10 people meet at a reunion and each person shake hands exactly once with each 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

thank you

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Kudos [?]: 615 [0], given: 32

Senior Manager
Joined: 07 Jan 2008
Posts: 286

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Re: PS probability or else? [#permalink]

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16 Jul 2008, 07:52
1
KUDOS
Stand these 10 people in a row and start counting from the left:
* The first person (from left) will shake 9 hands.
* The second person (from left) will shake 8 hands [Note: we have already counted the hand-shake with the person to his left]
* and so on.

So, you will get:
9 + 8 + 7 + 6 + ...+ 1 [Simple AP]
Sum = Average * Number of Terms
(9+1)/2 * 9 = 45
D

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Senior Manager
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Location: Eastern Europe
Schools: Oxford
Re: PS probability or else? [#permalink]

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16 Jul 2008, 13:15
2
KUDOS
Another approach:
Each of 10 persons shakes hands with 9 others => 10*9 handshakes.
Each handshake was counted twice => number of handshakes = 10*9/2 = 45.

Yet another approach: number of handshakes = C(2,10) = 45.

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Director
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Re: PS probability or else? [#permalink]

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16 Jul 2008, 17:33
greenoak wrote:
Another approach:
Each of 10 persons shakes hands with 9 others => 10*9 handshakes.
Each handshake was counted twice => number of handshakes = 10*9/2 = 45.

Yet another approach: number of handshakes = C(2,10) = 45.

you stole my solution

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GMAT Club Legend
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Re: If 10 people meet at a reunion and each person shake hands [#permalink]

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04 Aug 2017, 01:29
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 people meet at a reunion and each person shake hands   [#permalink] 04 Aug 2017, 01:29
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