BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Combinatorics - How many combinations out of two groups?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 76
Joined: Thu Feb 19, 2009 12:10 pmFollowed by: 2 members
Thanked: 3 times
by Bens4vcobra » Thu Jun 16, 2011 6:04 am
A 4 person task force is to be formed from 4 men and 3 women who work in Company G's HR dept. If there are to be 2 men and 2 women, how many different task forcers can be formed?
A)14
B)18 (correct answer)
C)35
D)56
E)144

I am trying to use the "anagram" method prefered by MGMAT but I must be doing something wrong because I cannot come up with the correct answer.
"It takes no ability to give effort. Toughness is not God-given; it's a choice. The discipline to execute is a habit." - Nick Saban
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Thu Jun 16, 2011 6:12 am
Bens4vcobra wrote:A 4 person task force is to be formed from 4 men and 3 women who work in Company G's HR dept. If there are to be 2 men and 2 women, how many different task forcers can be formed?
A)14
B)18
C)35
D)56
E)144
We can take the task of "building" a task force and break it into stages.

Stage 1: select the 2 women for the team
Stage 2: select the 2 men for the team

Stage 1: since the order of the selected women does not matter, this is a combination question.
There are 3 women, and we want to choose 2 of them.
This can be accomplished in 3C2 ways, which equals 3

Stage 2: since the order of the selected men does not matter, this is a combination question.
There are 4 men, and we want to choose 2 of them.
This can be accomplished in 4C2 ways, which equals 6

At this point, we can apply the Fundamental Counting Principle and find the product of the two stages to get (3)(6) = 18

So the answer is B

Cheers,
Brent

PS: To learn a shortcut for calculating combinations in your head, see https://youtu.be/-bbu2h-07iA
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1448
Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members
Location: India
Thanked: 375 times

by Frankenstein » Thu Jun 16, 2011 6:13 am
Hi,
From 4 men, 2 men can be selected in 4C2 = 6ways
From 3 women, 2 women can be selected in 3C2 = 3ways
So, number of different task force teams that can e formed is 6*3 = 18 ways.
Cheers!

Things are not what they appear to be... nor are they otherwise
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members
Location: Milpitas, CA
Thanked: 1854 times
GMAT Score:770

by Anurag@Gurome » Thu Jun 16, 2011 6:15 am
Bens4vcobra wrote:A 4 person task force is to be formed from 4 men and 3 women who work in Company G's HR dept. If there are to be 2 men and 2 women, how many different task forcers can be formed?
A)14
B)18 (correct answer)
C)35
D)56
E)144
Number of different task forces = (Number of ways to select 2 men out of 4)*(Number of ways to select 2 women out of 3) = (4C2)*(3C2) = 6*3 = 18

The correct answer is B.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 76
Joined: Thu Feb 19, 2009 12:10 pmFollowed by: 2 members
Thanked: 3 times

by Bens4vcobra » Thu Jun 16, 2011 7:09 am
Thanks all.

What does the "C2" mean? I've never seen this before...
"It takes no ability to give effort. Toughness is not God-given; it's a choice. The discipline to execute is a habit." - Nick Saban
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1560
Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members
Thanked: 137 times

by thephoenix » Thu Jun 16, 2011 7:30 am
Bens4vcobra wrote:Thanks all.

What does the "C2" mean? I've never seen this before...
C stands for combination
P stands for permutation

nCr means n!/(r!*(n-r)!)
4C2=4!(2!*(4-2)!)=4!/(2!*2!)

similarly
npr n!/(n-r)!
Many of the great achievements of the world were accomplished by tired and discouraged men who kept on working
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 76
Joined: Thu Feb 19, 2009 12:10 pmFollowed by: 2 members
Thanked: 3 times

by Bens4vcobra » Thu Jun 16, 2011 8:03 am
thephoenix wrote:
Bens4vcobra wrote:Thanks all.

What does the "C2" mean? I've never seen this before...
C stands for combination
P stands for permutation

nCr means n!/(r!*(n-r)!)
4C2=4!(2!*(4-2)!)=4!/(2!*2!)

similarly
npr n!/(n-r)!
Ah so its just an abreviation for using the combinatorics formula. Thanks.
"It takes no ability to give effort. Toughness is not God-given; it's a choice. The discipline to execute is a habit." - Nick Saban
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1