• Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors

Permutation Combination

This topic has 1 expert reply and 5 member replies
Nidhs Senior | Next Rank: 100 Posts Default Avatar
Joined
06 Jan 2008
Posted:
69 messages
Followed by:
1 members
Upvotes:
3

Permutation Combination

Post Fri Feb 08, 2008 6:09 pm
A five-member committee is to be formed from a group of five military officers and nine civilians. If the committee must include at least two officers and two civilians, in how many different ways can the committee be chosen?


119

1,200

3,240

3,600

14,400

Can someone slove this for me?

  • +1 Upvote Post
  • Quote
  • Flag
Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
senthil Master | Next Rank: 500 Posts Default Avatar
Joined
23 Dec 2007
Posted:
188 messages
Upvotes:
4
Top Reply
Post Tue Feb 12, 2008 12:00 pm
Choosing the military officer as the fifth person coz there will be atleast two officers and two civilians in the five member committee.
5c2.9c2.3 ....( out of 5 officers two are selected rest is just 3 officers)
Choosing the civilians as the fifth person coz there will be atleast two officers and two civilians in the five member committee.
5c2.9c2.7 ....( out of 10civilians two are selected rest is just 7 civilians)

THEREFORE 5c2.9c2.3+5c2.9c2.7=5c2.9c2.10=3600ways

Thanks
Senthil

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Stuart Kovinsky GMAT Instructor
Joined
08 Jan 2008
Posted:
3225 messages
Followed by:
608 members
Upvotes:
1710
GMAT Score:
800
Top Reply
Post Tue Feb 12, 2008 2:28 pm
GMATDUD wrote:
I used a different approach and did get a different answer.

2 oficers from 5 can be selected in 5c2 ways = 10
2 civilians can be selected in 9c2 ways = 36
the remaining can be either officer or civilian and there are 10 people (7 civilians and 3 officers) left - that makes 10 c 1 ways = 10

hence 10*10*36 = 3600 ways.

Your approach seems logical Luv, but I am curious whats wrong in the approach I took .. should fit rite in with the requirement.

NIDS , whats the ans?
The problem with this approach is that it will give a lot of duplicate solutions.

For example, you'll have combinations in which you chose officers A and B in your first selection and then officer C in your final selection. You'll have other combinations in which you chose officers A and C in your first selection and then officer B in your final selection. You've counted each of these as a separate possibility, when in fact they're identical.

Luvaduva's solution is perfect!

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test under Proctored Conditions! - Find a practice test near you or live and online in Kaplan's Classroom Anywhere environment. Register today!
senthil Master | Next Rank: 500 Posts Default Avatar
Joined
23 Dec 2007
Posted:
188 messages
Upvotes:
4
Post Tue Feb 12, 2008 12:00 pm
Choosing the military officer as the fifth person coz there will be atleast two officers and two civilians in the five member committee.
5c2.9c2.3 ....( out of 5 officers two are selected rest is just 3 officers)
Choosing the civilians as the fifth person coz there will be atleast two officers and two civilians in the five member committee.
5c2.9c2.7 ....( out of 10civilians two are selected rest is just 7 civilians)

THEREFORE 5c2.9c2.3+5c2.9c2.7=5c2.9c2.10=3600ways

Thanks
Senthil

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Stuart Kovinsky GMAT Instructor
Joined
08 Jan 2008
Posted:
3225 messages
Followed by:
608 members
Upvotes:
1710
GMAT Score:
800
Post Tue Feb 12, 2008 2:28 pm
GMATDUD wrote:
I used a different approach and did get a different answer.

2 oficers from 5 can be selected in 5c2 ways = 10
2 civilians can be selected in 9c2 ways = 36
the remaining can be either officer or civilian and there are 10 people (7 civilians and 3 officers) left - that makes 10 c 1 ways = 10

hence 10*10*36 = 3600 ways.

Your approach seems logical Luv, but I am curious whats wrong in the approach I took .. should fit rite in with the requirement.

NIDS , whats the ans?
The problem with this approach is that it will give a lot of duplicate solutions.

For example, you'll have combinations in which you chose officers A and B in your first selection and then officer C in your final selection. You'll have other combinations in which you chose officers A and C in your first selection and then officer B in your final selection. You've counted each of these as a separate possibility, when in fact they're identical.

Luvaduva's solution is perfect!

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test under Proctored Conditions! - Find a practice test near you or live and online in Kaplan's Classroom Anywhere environment. Register today!
GMATDUD Senior | Next Rank: 100 Posts Default Avatar
Joined
16 Jan 2007
Posted:
62 messages
Post Mon Feb 11, 2008 8:52 pm
David,

we are only looking at # of ways in the third category and not looking at the probability. there are 10 folks left and we need 1 to fill the position . it could be either C or O. That was the reasoning in doing a 10C1.

  • +1 Upvote Post
  • Quote
  • Flag
davidforsberg Junior | Next Rank: 30 Posts Default Avatar
Joined
05 Feb 2008
Posted:
16 messages
Upvotes:
3
Test Date:
21/2
Target GMAT Score:
650
Post Mon Feb 11, 2008 12:43 pm
I agree on this one with luvaduva, DUD, regarding your approach I don't think it's right because there are 7 Civilians and 3 Officers left, which would not give an equal probability between them, and from what I understand is that with C and V you cannot mix different variables. If I'm wrong, someone please correct me.

_________________
T minus 17 hours

  • +1 Upvote Post
  • Quote
  • Flag

Best Conversation Starters

1 lheiannie07 112 topics
2 swerve 64 topics
3 LUANDATO 64 topics
4 ardz24 61 topics
5 AAPL 57 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

227 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

176 posts
3 image description Jeff@TargetTestPrep

Target Test Prep

168 posts
4 image description Rich.C@EMPOWERgma...

EMPOWERgmat

138 posts
5 image description GMATGuruNY

The Princeton Review Teacher

129 posts
See More Top Beat The GMAT Experts