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m07 #27

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Intern
Joined: 03 Oct 2012
Posts: 10
Location: India
Concentration: General Management, Entrepreneurship
Schools: Tepper '16 (S)
GMAT 1: 620 Q50 V25
GMAT 2: 680 Q50 V31
GRE 1: 314 Q166 V148
GPA: 3.44
WE: Operations (Computer Software)

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15 Aug 2013, 10:47
Every B.E meets every other person!
10(ways to select a B.E)*16(selecting one other person from the whole = 160

Every C meets every B.E
10*7 = 70

Total= 160+70=330

But our answer should be independent of order, i.e., A meeting B, is same as B meeting A.

Hence correct answer is total / 2

Hence
115

---------------------

bipolarbear wrote:
10 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?

(A) 144
(B) 131
(C) 115
(D) 90
(E) 45

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

[Reveal] Spoiler: OE
Chairmen shake hands 10*7=70 with business executives times. Business executives shake hands with each other 10 C 2 times or 45 times. The total is 115 .

Can someone explain to me why its 10 C 2?
Intern
Joined: 30 May 2013
Posts: 13

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15 Aug 2013, 15:14
hello,

could someone please explain this one thing to me.

When 10 execs shake hand with each other we say 10*9/2 as the order does no matter.

But when we do 7 chairman shaking hands with 10 execs, we are saying 7*10. Why aren't we dividing this by 2?

Intern
Joined: 13 Aug 2013
Posts: 23

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16 Aug 2013, 02:03
Hand Shakes among the business executive and chairmen - 10c1 x 7c1 = 70
Hand Shakes among the executives alone- 10c2 =45
total- 115 hand shakes
Intern
Joined: 13 Aug 2013
Posts: 23

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16 Aug 2013, 02:12
1
KUDOS
makhija1 wrote:
hello,

could someone please explain this one thing to me.

When 10 execs shake hand with each other we say 10*9/2 as the order does no matter.

But when we do 7 chairman shaking hands with 10 execs, we are saying 7*10. Why aren't we dividing this by 2?

This is essentially because executives and a chairmen are a different set of people. We are just selecting one from each group (selecting one from executives 10c1 and one from chirmen 7c1) . And hence the cases. 10c1 x 7c1. Whereas executives is a single group and we need to select two people from the same group for the handshake, hence 10c2
Intern
Joined: 13 Aug 2013
Posts: 23

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01 Aug 2014, 00:21
10c2(executives among themselves) +10x7 (executives and chairmen)=115
Intern
Joined: 22 Jul 2014
Posts: 4
Concentration: Finance, General Management
GMAT 1: 680 Q49 V35
GPA: 2.8
WE: Other (Energy and Utilities)

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01 Aug 2014, 02:47
bipolarbear wrote:
10 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?

(A) 144
(B) 131
(C) 115
(D) 90
(E) 45

Can someone explain to me why its 10 C 2?

This question deals with the concept of "Combination". The difference between Permutation and Combination is that in Combination "order" does not matter. Say, if A is shaking hands with B, it's equivalent to B shaking hands with A and either of the event shall be counted as One only. Similarly, in case of A, B & C, the no of "orders" possible is 3 C 2 = 3 ( A & B, B & C and A & C). So this type of counting is done using formula nCr, where n is total no of participants and r is no. of participants in one activity.

Accordingly, when there are 10 people, while 2 shake hands at a time, total no of possible is 10 C 2.
Intern
Joined: 15 Sep 2013
Posts: 44
Concentration: Strategy, Entrepreneurship
GMAT 1: 680 Q47 V36
GMAT 2: 740 Q50 V40
GPA: 3.65

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01 Aug 2014, 10:59
gurpreetsingh wrote:
Another method

17 c 2 - 7 c 2 = 115

17 c 2 = total number of hand shakes between 17 people
7 c 2 = total number of hand shakes between chairmen

Nice way to solve the question in less time....
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Re: m07 #27   [#permalink] 01 Aug 2014, 10:59

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