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To furnish a room in a model home, an interior decorator has

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Intern
Intern
Joined: 09 Jun 2006
Posts: 14
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To furnish a room in a model home, an interior decorator has [#permalink] New post 11 Sep 2006, 17:43
To furnish a room in a model home, an interior decorator has to select 2 tables and 2 chairs from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and 150 different combos are possible, how many different tables are in the warehouse?
Intern
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Joined: 07 Jan 2006
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Location: Tacoma, WA
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 [#permalink] New post 11 Sep 2006, 18:02
6

let x = # tables

we know

xC2 * 5C2 = 150

so

[x!/((x-2)!*2!)]*[5!/(3!*2!)] = 150

[(x*(x-1)*(x-2)!)/((x-2)!*2!)]*[(5*4*3!)/(3!*2!)] = 150

[(x*(x-1))/2!]*[20/2!] = 150

5(x*(x-1)) = 150

x^2 - x - 30 = 0

(x-6)(x+5) = 0

x = 6
Director
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Joined: 23 Jun 2005
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 [#permalink] New post 11 Sep 2006, 18:35
Arrived at 6, the same way as jd04
  [#permalink] 11 Sep 2006, 18:35
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To furnish a room in a model home, an interior decorator has

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