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# Two members of a club are to be selected to represent the

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Director
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Two members of a club are to be selected to represent the [#permalink]

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17 Sep 2006, 17:22
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Two members of a club are to be selected to represent the club at a national meeting. If there are 190 different possible selections of the 2 members, how many members does the club have?

a. 20
b. 27
c. 40
d. 57
e. 95
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VP
Joined: 25 Jun 2006
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17 Sep 2006, 21:00
.
.
.
.
.

you get the equation x^2 -x - 380 = 0.

try the answers, and u get A.
Director
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17 Sep 2006, 23:15
Yeah - here you have nC2 = 190.

Figure out n by plugging in numbers.
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Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?

Intern
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17 Sep 2006, 23:17
This is a combinations thing (ie the order in which the members are picked does not matter). The number of ways in which 2 members can be picked is 190, so:

(x!)
190 = ------------
(2!)*(x-2)!

which can be worked to:

380 = x*(x-1)

Then plug away! Since the answers are given in increasing value start with the middle one (C). You get 40*39 which is >1000 so then move "up" to a smaller answer. Anwers B ia also too big. Then finally to A. 20*19 = 380 so the answer is A. By starting in the middle you know which way to move ("up" or "down") and that way you only need to plug in 3 out of the 5 answers, saving a little time.
Intern
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17 Sep 2006, 23:20
crap sorry about the formatting of the first equation:

190 = (x!)/[2!*(x-2)!]
Director
Joined: 28 Dec 2005
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17 Sep 2006, 23:35
Two members of a club are to be selected to represent the club at a national meeting. If there are 190 different possible selections of the 2 members, how many members does the club have?

a. 20
b. 27
c. 40
d. 57
e. 95

straight A. 20C2 = 190
Manager
Joined: 14 Sep 2006
Posts: 198
Schools: Olin Business School - Washington University
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18 Sep 2006, 00:13
A.

n=20
r=2

Combination, order doesnt matter...

n!/(n-r)!(r!)
= (20!)/(18!)(2!)
= 20x19/2
= 380/2
= 190
18 Sep 2006, 00:13
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