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A small company employs 3 men and 5 women. If a team of 4

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Manager
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Joined: 04 May 2009
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Location: London
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A small company employs 3 men and 5 women. If a team of 4 [#permalink] New post 23 May 2010, 11:11
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A
B
C
D
E

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  15% (low)

Question Stats:

83% (02:07) correct 17% (01:16) wrong based on 53 sessions
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

A. 1/14
B. 1/7
C. 2/7
D. 3/7
E. 1/2

I find the explanation provided in MGMAT very complicated and would like to know what techniques other people would recommend to solve this problem in 2 mins.
[Reveal] Spoiler: OA

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Re: Proba and combinations (MGMAT) [#permalink] New post 23 May 2010, 11:32
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lets see

Total amount of possible choices is

8! / 4! 4! = 8 x 6 x 7 x 5 / 4 x 3 x 2 = 70
the only way to have exactly 2 women is to have 2 men so the number of ways we can select 2men from 4 is

3!/ 2! = 3

the number of ways we can select 2 women from 5 is

5! /2! 3! = 5 x 4 / 2 = 10

the total different ways you can have 2 women and 2 men

3 x 10 = 30

desired outcome / total outcomes = probability -> 30 / 70 = 3/7

so it should be D



pS. Kudos are always welcomed :wink:
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Re: Proba and combinations (MGMAT) [#permalink] New post 23 May 2010, 11:37
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nifoui wrote:
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
A: 1/14
B: 1/7
C: 2/7
D: 3/7
E: 1/2

I find the explanation provided in MGMAT very complicated and would like to know what techniques other people would recommend to solve this problem in 2 mins.

Will post OA later.


P=Favorable outcomes / Total # of outcomes

Favorable outcomes: 2 women and 2 men = C^2_5*C^2_3=30;
Total # of outcomes: 4 people out of 5+3=8 = C^4_8=70;

P=\frac{30}{70}=\frac{3}{7}.

Answer: D.
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Manager
Manager
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Joined: 04 May 2009
Posts: 132
Location: London
Schools: Haas (WL), Kellogg (matricultating), Stanford (R2, ding), Columbia (ding)
WE 1: 3 years hotel industry sales and marketing France
WE 2: 3 years financial industry marketing UK
Followers: 2

Kudos [?]: 20 [0], given: 10

Re: Proba and combinations (MGMAT) [#permalink] New post 23 May 2010, 13:47
Thank you both!

AO is D indeed :)
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Re: A small company employs 3 men and 5 women. If a team of 4 [#permalink] New post 29 Nov 2013, 05:58
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Re: A small company employs 3 men and 5 women. If a team of 4   [#permalink] 29 Nov 2013, 05:58
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