GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2018, 16:51

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

Moderator
Joined: 22 Jun 2014
Posts: 1034
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
Re: A small company employs 3 men and 5 women. If a team of 4  [#permalink]

Show Tags

09 Apr 2016, 02:31
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

if there are exactly two women in the team then other to two will be the men.

So we have to choose 2 women out of 5 and 2 men out of 3. and total 4 out of 8.

Probability = 3c2 * 5c2 / 8c4 = 30/(10*7) = 3/7
_________________

---------------------------------------------------------------
Target - 720-740
http://gmatclub.com/forum/information-on-new-gmat-esr-report-beta-221111.html
http://gmatclub.com/forum/list-of-one-year-full-time-mba-programs-222103.html

Manager
Joined: 20 Jan 2017
Posts: 60
Location: United States (NY)
Schools: CBS '20 (A)
GMAT 1: 750 Q48 V44
GMAT 2: 610 Q34 V41
GPA: 3.92
Re: A small company employs 3 men and 5 women. If a team of 4  [#permalink]

Show Tags

25 Feb 2017, 09:26
1) The total number of 4 people combinations selected from 3+5=8 people - Combination: 8!/4!(8-4)!=8*7*6*5/4*3*2=7*2*5=70
2) The probability that there will be exactly two women: First woman can be any one of the 5; second woman - one of the remaining 4; first man - one of the 3; second man - one of the 2: 5*4*3*2=120. Since it does not matter the order of women and men we have to divide each category by 2: 5*4/2=10; 3*2/2=3; 10*3=30
3) Probability that there will be exactly 2 women in a group is 30/70=3/7

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: A small company employs 3 men and 5 women. If a team of 4  [#permalink]

Show Tags

14 Dec 2017, 10:13
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

We need to determine the probability that when 4 employees are selected from 3 men and 5 women, 2 women and 2 men will be selected.

Let’s determine the number of ways to select the 2 women and 2 men.

Number of ways to select 2 women:

5C2 = (5 x 4)/2! = 10

Number of ways to select 2 men:

3C2 = (3 x 2)/2! = 3

Thus, 2 men and 2 women can be selected in 10 x 3 = 30 ways.

Finally, we can determine the number of ways to select 4 people from 8.

8C4 = 8! / [4! x (8-4)!] = (8x 7 x 6 x 5)/4! = (8 x 7 x 6 x 5)/(4 x 3 x 2) = 7 x 2 x 5 = 70

Thus, the probability is 30/70 = 3/7.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 08 Dec 2017
Posts: 17
Re: A small company employs 3 men and 5 women. If a team of 4  [#permalink]

Show Tags

14 Dec 2017, 17:50
redfield wrote:
Can someone explain to me why the answer is not 1/7?

I did Desired Outcomes/Total Outcomes. Obviously total is 70 we all agree on that. We also all agree that 5 women choose 2 = 10.

However, I don't see why we then do 3 men choose 2. Why does it matter which men are chosen?

Can someone explain logically rather than mathematically?

You agree there are 70 possible groups. It matters what men are chosen because they form more groups. Let's assume the three men are A,B, and C. For each of the 10 female pairs chosen two men have to be chosen (one man has to be left out. So for a given female pair the left out man could be A,B, or C. When you don't multiply 10 by 3 you're basically asserting female pair A B, female pair A C, and female pair B C are the same group.

Posted from my mobile device
Intern
Joined: 01 Nov 2017
Posts: 11
Re: A small company employs 3 men and 5 women. If a team of 4  [#permalink]

Show Tags

06 Jan 2018, 09:35
x2suresh wrote:
$$P=\frac{3C2*5C2}{8C4}$$

Could someone please explain the way how to solve this fraction mathematically? What does C2 and C4 stand for? What calculations are derived from this?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 49858
Re: A small company employs 3 men and 5 women. If a team of 4  [#permalink]

Show Tags

06 Jan 2018, 10:17
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12649
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A small company employs 3 men and 5 women. If a team of 4  [#permalink]

Show Tags

12 Jan 2018, 14:01
Hi All,

You did the first 'step' of this question correctly. The number of groups of 2 men IS 3 and the number of groups of 2 women IS 10. Now, you have to do the rest of the math in a really specific way:

Since each "subgroup" of men can be paired with each "subgroup" of women, there are (3)(10) = 30 possible groups of four that include exactly 2 women. Since this is a probability question, we now have to determine the total number of groups of four that are possible...

That is 8C4 = (8)(7)(6)(5) / (4)(3)(2)(1) = (2)(7)(1)(5) = 70 possible groups of 4

30/70 = 3/7

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Re: A small company employs 3 men and 5 women. If a team of 4 &nbs [#permalink] 12 Jan 2018, 14:01

Go to page   Previous    1   2   [ 27 posts ]

Display posts from previous: Sort by