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

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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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71% (02:16) correct 29% (01:31) wrong based on 107 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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Joined: 04 May 2009
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Location: London
Schools: Haas (WL), Kellogg (matricultating), Stanford (R2, ding), Columbia (ding)
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Followers: 2

Kudos [?]: 29 [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] New post 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] New post 28 Nov 2014, 04:11
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A small company employs 3 men and 5 women. If a team of 4   [#permalink] 28 Nov 2014, 04:11
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