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Among 200 programmers working for an IT company, 30% know

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CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City
Among 200 programmers working for an IT company, 30% know [#permalink]

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06 Nov 2007, 15:02
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Among 200 programmers working for an IT company,
30% know C++
80% know VB
10% neither

In how many ways can a team of three programmers, all knowing both C++ and VB be formed?

2960
3990
6840
8820
9880
SVP
Joined: 29 Aug 2007
Posts: 2473

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06 Nov 2007, 17:55
bmwhype2 wrote:
Among 200 programmers working for an IT company,
30% know C++
80% know VB
10% neither

In how many ways can a team of three programmers, all knowing both C++ and VB be formed?

2960
3990
6840
8820
9880

20% of 200 = 40. so it is 40c3.

= 40c3
= (40x39x38x37!) / (3!x37!)
= (40x39x38x37!) / (3x2)
= (20x13x38)
= 9880 (should be without calculating)
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

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06 Nov 2007, 18:26
Using venn diagram:
#(only know c++) = 60-x
#(know both c++ and vb) = x
#(know VB) = 160-x
#(know neither) = 20

60-x + x + 160-x + 20 = 200
x = 40

# of 3 men team that can be formed from a group of 40 = 40C3 = 9880
Director
Joined: 09 Aug 2006
Posts: 755

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06 Nov 2007, 22:18
bmwhype2 wrote:
Among 200 programmers working for an IT company,
30% know C++
80% know VB
10% neither

In how many ways can a team of three programmers, all knowing both C++ and VB be formed?

2960
3990
6840
8820
9880

Those who know both:
200 - 20 = 60 + 160 - Both
Both = 40

Senior Manager
Joined: 16 Apr 2006
Posts: 277

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18 Dec 2007, 14:14
Darden2010 wrote:
overlaping set = 20%
20%*200 =40

ways 40 people can be arranged without repetition into groups of 3:
40!/(3!*37!) = (38*39*40)/(1*2*3) = 9880

Cheers!

I also have same approach.
_________________

Trying hard to achieve something unachievable now....

Director
Joined: 08 Jun 2007
Posts: 573

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18 Dec 2007, 20:18
wow a question testing sets as well as combinations skills
true combination question !
Manager
Joined: 03 Sep 2006
Posts: 233

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18 Dec 2007, 21:06
Late, but C:

T = 1 + 2 - both + neither
200 = 60 + 160 - x + 20
x = 40

40C3 = 9880
18 Dec 2007, 21:06
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