Find all School-related info fast with the new School-Specific MBA Forum

It is currently 03 Aug 2015, 05:12
GMAT Club Tests

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A 4-person task force is to be formed from the 4 men and 3 w

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 10 Jul 2009
Posts: 43
Location: Beijing
Followers: 1

Kudos [?]: 14 [0], given: 3

A 4-person task force is to be formed from the 4 men and 3 w [#permalink] New post 13 Jul 2009, 11:19
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

92% (01:38) correct 8% (01:05) wrong based on 132 sessions
A 4-person task force is to be formed from the 4 men and 3 women who work in Company G's human resources department. If there are to be 2 men and 2 women on this task force, how many different task forces can be formed?

A. 14
B. 18
C. 35
D. 56
E. 144
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Dec 2013, 05:00, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
4 KUDOS received
Current Student
User avatar
Joined: 03 Aug 2006
Posts: 116
Location: Next to Google
Schools: Haas School of Business
Followers: 4

Kudos [?]: 157 [4] , given: 3

Re: 4 person task force GMAT Prep problem [#permalink] New post 13 Jul 2009, 13:00
4
This post received
KUDOS
1
This post was
BOOKMARKED
The answer is B.

This is a combinations problem.

\(C^n_k = \frac{n!}{k!(n-k)!}\)

where \(n\) = total number of items available to select and \(k\) = number of items to be selected.

In this problem there are two distinct sets: 1 set of men and 1 set of women.

The number of ways we can select 2 (\(k\)) men from a total of 4 (\(n\)) men:

\(\Rightarrow C^n_k = \frac{n!}{k!(n-k)!}\)

\(\Rightarrow C^4_2 = \frac{4!}{2!(4-2)!}\)

\(\Rightarrow C^4_2 = \frac{4!}{2!2!}\)

\(\Rightarrow C^4_2 = \frac{4 \times 3}{2 \times 1} = 6\)

Similarly the number of ways we can select 2 (\(k\)) women from a total of 3 (\(n\)) women:

\(\Rightarrow C^n_k = \frac{n!}{k!(n-k)!}\)

\(\Rightarrow C^3_2 = \frac{3!}{2!(3-2)!}\)

\(\Rightarrow C^3_2 = \frac{3!}{2!1!}\)

\(\Rightarrow C^3_2 = 3\)

Total number of different task forces of 2 men and 2 women possible:

\(= 6 \times 3\)

\(= 18\)
Senior Manager
Senior Manager
avatar
Joined: 25 Mar 2009
Posts: 305
Followers: 6

Kudos [?]: 119 [0], given: 6

Re: 4 person task force GMAT Prep problem [#permalink] New post 13 Jul 2009, 13:37
nookway's calcs are good.

Just one note about why we are using the nCr formula.

Let's label the 4 men M1, M2, M3, and M4. One possible combo is if you first choose M1, then choose M2. This team of M1 and M2 is the same as if you had chosen M2 first, then M1 second. So since M1M2 is not distinct from M2M1, order does not matter. When order does not matter, use the combination formula.
Intern
Intern
avatar
Joined: 10 Jul 2009
Posts: 43
Location: Beijing
Followers: 1

Kudos [?]: 14 [0], given: 3

Re: 4 person task force GMAT Prep problem [#permalink] New post 13 Jul 2009, 13:39
Thanks a lot!

I was looking at it as being much more complicated than it actually was.

Sorry, the OA was indeed 18.
Manager
Manager
avatar
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 235
Schools: Johnson '15
Followers: 2

Kudos [?]: 33 [0], given: 16

Re: 4 person task force GMAT Prep problem [#permalink] New post 03 Jul 2011, 00:20
do we need to think as they are two independent events and
to select 2 seats from 4 men is 6 and similarly to filll 2 seats from 3 women is 3....
so it is 6X3 = 18?
_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat ;)

Satyameva Jayate - Truth alone triumphs

Manager
Manager
User avatar
Joined: 12 Jan 2013
Posts: 249
Followers: 3

Kudos [?]: 39 [0], given: 47

GMAT ToolKit User
Re: 4 person task force GMAT Prep problem [#permalink] New post 10 Dec 2013, 04:51
Hi,

wouldn't it suffice if we simply used 4!/2! for men and added that to 3!/1! for women?


4!/2! = 4x3 = 12
3!/1! = 6

12 + 6 = ways 4 men can fill 2 positions + ways 3 women can fill 2 positions = 18.

Why would this NOT work in general (because it works in this specific case), and why would we need to use relatively "complicated" divisions nCr formulas when the solution is much more straightforward than that?
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28784
Followers: 4596

Kudos [?]: 47570 [1] , given: 7130

Re: 4 person task force GMAT Prep problem [#permalink] New post 10 Dec 2013, 05:07
1
This post received
KUDOS
Expert's post
aeglorre wrote:
A 4-person task force is to be formed from the 4 men and 3 women who work in Company G's human resources department. If there are to be 2 men and 2 women on this task force, how many different task forces can be formed?

A. 14
B. 18
C. 35
D. 56
E. 144

Hi,

wouldn't it suffice if we simply used 4!/2! for men and added that to 3!/1! for women?


4!/2! = 4x3 = 12
3!/1! = 6

12 + 6 = ways 4 men can fill 2 positions + ways 3 women can fill 2 positions = 18.

Why would this NOT work in general (because it works in this specific case), and why would we need to use relatively "complicated" divisions nCr formulas when the solution is much more straightforward than that?


What is the logic behind 4!/2! and 3!/1!?

The number of ways to choose 2 men out of 4 is \(C^2_4=6\);
The number of ways to choose 2 women out of 3 is \(C^2_3=3\).

Principle of Multiplication says that if one event can occur in \(m\) ways and a second can occur independently of the first in \(n\) ways, then the two events can occur in \(mn\) ways.

Thus the number of ways to choose 2 men AND 2 women is 6*3=18.

Answer: B.

Theory on Combinations: math-combinatorics-87345.html

DS questions on Combinations: search.php?search_id=tag&tag_id=31
PS questions on Combinations: search.php?search_id=tag&tag_id=52

Tough and tricky questions on Combinations: hardest-area-questions-probability-and-combinations-101361.html

_________________

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
User avatar
Joined: 19 Mar 2013
Posts: 23
Followers: 0

Kudos [?]: 2 [0], given: 27

Re: A 4-person task force is to be formed from the 4 men and 3 w [#permalink] New post 12 Dec 2013, 05:46
we can chose 2 women out of 3 in 3C2 ways = 3
2 men out of 4 in 4C2 ways = 6

different combinations of 6 men and 3 women = 6*3= 18
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5722
Followers: 323

Kudos [?]: 63 [0], given: 0

Premium Member
Re: A 4-person task force is to be formed from the 4 men and 3 w [#permalink] New post 14 Mar 2015, 19:05
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: A 4-person task force is to be formed from the 4 men and 3 w   [#permalink] 14 Mar 2015, 19:05
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic From a total of 5 boys and 4 girls, how many 4-person committees can Bunuel 5 26 Mar 2015, 03:21
1 Find the probability that a 4 person committee chosen at ran delta09 2 14 Dec 2009, 20:05
10 Experts publish their posts in the topic In a 4 person race, medals are awarded to the fastest 3 runn kirankp 13 03 Dec 2009, 06:52
3 Experts publish their posts in the topic In a 4 person race, medals are awarded to the fastest 3 runn rathoreaditya81 6 20 Nov 2009, 01:53
28 Experts publish their posts in the topic In a 4 person race, medals are awarded to the fastest 3 runn 12345678 10 18 Sep 2007, 22:32
Display posts from previous: Sort by

A 4-person task force is to be formed from the 4 men and 3 w

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.