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GMAT PREP combination question

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GMAT PREP combination question [#permalink] New post 11 Jan 2007, 15:06
Any clues guys

To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehoues and if 150 different combinations are possible, how many tables are in the warehouse?

a) 6
b) 8
c) 10
d) 15
e) 30

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 [#permalink] New post 11 Jan 2007, 16:39
-A-

5C2 = 10
TC2 = T!/[2!(T-2)!] -- (1)

10 * (1) = 150 --> TC2=15. Solve (1) using the answers to get 15:

6 ---> 6C2= 15

10*15=150 ---> Bingo

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 [#permalink] New post 12 Jan 2007, 19:12
5C2 * nC2 = 10 * nC2 = 150 => nC2 = 15.

nC2 = n*(n-1)/2 = 15 => n = 6.

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 [#permalink] New post 22 Feb 2007, 01:36
Quick question:

How was this formula obtained?

nC2 = n*(n-1)/2

Is this another formula for getting a combination?
  [#permalink] 22 Feb 2007, 01:36
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