A small company employs 3 men and 5 women. If a team of 4 : GMAT Problem Solving (PS)
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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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A small company employs 3 men and 5 women. If a team of 4 [#permalink]

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23 May 2010, 11:11
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Difficulty:

25% (medium)

Question Stats:

71% (02:20) correct 29% (01:32) wrong based on 163 sessions

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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]

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23 May 2010, 11:32
5
KUDOS
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
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Ps. Kudos are always welcomed ; )

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Re: Proba and combinations (MGMAT) [#permalink]

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23 May 2010, 11:37
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Expert's post
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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 = $$C^4_8=70$$;

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

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Manager
Joined: 04 May 2009
Posts: 130
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: 3

Kudos [?]: 48 [0], given: 10

Re: Proba and combinations (MGMAT) [#permalink]

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23 May 2010, 13:47
Thank you both!

AO is D indeed
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Yes I can!

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Re: A small company employs 3 men and 5 women. If a team of 4 [#permalink]

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29 Nov 2013, 05:58
Hello from the GMAT Club BumpBot!

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Re: A small company employs 3 men and 5 women. If a team of 4 [#permalink]

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28 Nov 2014, 01:09
Bunuel,i did not understand why we took two men too?I did it like Favorable outcomes: selecting 2 women C^2_5
and Total # of outcomes: 4 people out of 5+3=8 = C^4_8=70;
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Re: A small company employs 3 men and 5 women. If a team of 4 [#permalink]

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28 Nov 2014, 04:11
Ralphcuisak wrote:
Bunuel,i did not understand why we took two men too?I did it like Favorable outcomes: selecting 2 women C^2_5
and Total # of outcomes: 4 people out of 5+3=8 = C^4_8=70;

The team should have 4 employees out of which 2 are women, thus the remaining 2 will be men.
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Re: A small company employs 3 men and 5 women. If a team of 4 [#permalink]

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19 Apr 2016, 02:14
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A small company employs 3 men and 5 women. If a team of 4   [#permalink] 19 Apr 2016, 02:14
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