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

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 Post subject: Two members of a club are to be selected to represent the
 Post Posted: Mon Jun 16, 2008 2:53 am 
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?

20
27
40
57
95

This is probably super easy but I don't seem to find the solution. Thanks!
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Mike
 Post subject:
 Post Posted: Tue Jun 17, 2008 4:07 pm 
Let's say n is the number of members in the club.

There are 190 ways to select 2 members out of n.

n! / (2! * (n-2)!) = 190

n * (n-1) = 190 * 2!

n * (n-1) = 380

380 = 2*2*5*19 = 20 * 19

Answer: A (20 members)
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StaceyKoprince
 Post subject:
 Post Posted: Thu Jun 26, 2008 2:56 am 
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ManhattanGMAT Staff


Posts: 5788
Location: San Francisco
You can also try the answer choices. Let's say you decide to start in the middle:

If there are 40 members and 2 are selected, you'd set up this equation:
40!/[2!38!] = (40*39*38!)/(2*38!) = 40*39/2 = 20*39. Eyeball it - does that equal 190? No, it's too big. Try a smaller number. And so on, until you get the right answer!

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Stacey Koprince
Instructor
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ManhattanGMAT
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