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

It is currently 24 Apr 2014, 03:09

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

Permutation and Combination Help!

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
Joined: 16 Mar 2011
Posts: 2
Followers: 0

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

Permutation and Combination Help! [#permalink] New post 16 Mar 2011, 05:18
Hi, I'm new to this site so forgive me if I violate any rules.

I need help with a P&C question:

A group of 10 people consists of 3 married couples and 4 single men.
A committee of 4 is to be fo from the 10 people.
How many different committees can be formed if the committee can consist of at most 1 married couple?

Would appreciate it if any one of you can reply asap! I need urgent help :(
Director
Director
Status: -=GMAT Jedi=-
Joined: 04 Jan 2011
Posts: 741
Location: Kochi, India
Schools: ISB
WE 1: Engineer - Larsen & Toubro, ECC Division
WE 2: Faculty - T.I.M.E.
Followers: 29

Kudos [?]: 116 [0], given: 66

GMAT Tests User
Re: Permutation and Combination Help! [#permalink] New post 16 Mar 2011, 08:11
Post Edit

Solution provided by me was wrong :P

Sorry!
_________________

Mission: Be a force of good and make a positive difference to every life I touch!

From 650 to 710 to 750 - My Tryst With GMAT [Experience Thread]


Last edited by Entwistle on 19 Mar 2011, 16:02, edited 1 time in total.
Director
Director
Status: -=GMAT Jedi=-
Joined: 04 Jan 2011
Posts: 741
Location: Kochi, India
Schools: ISB
WE 1: Engineer - Larsen & Toubro, ECC Division
WE 2: Faculty - T.I.M.E.
Followers: 29

Kudos [?]: 116 [0], given: 66

GMAT Tests User
Re: Permutation and Combination Help! [#permalink] New post 16 Mar 2011, 08:14
From next time on, post the questions for problem solving in this Forum:

gmat-problem-solving-ps-140/

Welcome to the Club :beer:

Enjoy your stay!
_________________

Mission: Be a force of good and make a positive difference to every life I touch!

From 650 to 710 to 750 - My Tryst With GMAT [Experience Thread]

GMAT Pill Instructor
User avatar
Joined: 14 Apr 2009
Posts: 1367
Location: New York, NY
Followers: 257

Kudos [?]: 553 [0], given: 5

Re: Permutation and Combination Help! [#permalink] New post 17 Mar 2011, 13:56
Expert's post
Hi yogibearsayshi,

This video might help you understand the breakdown of this "nested GMAT combination" question.
Image

Entwistle --good job breaking down the problem and doing the problem! But watch out! Your calculations were great, but looks like you forgot to get back to the original question and note that they only care about combinations that involve AT MOST 1 couple. I know--GMAT guys do that a lot. I almost missed it too! They make you do this complicated calculation that makes you forget what specific condition they restrict the problem to.

This video might help you understand combinations and permutations in general.
Image

Hope that helps!
_________________


... and more


Image What's Inside GMAT Pill?

Zeke Lee, GMAT Pill Study Method (Study Less. Score More.)


GMAT Pill Reviews | GMAT PILL Free Practice Test

Intern
Intern
Joined: 16 Mar 2011
Posts: 2
Followers: 0

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

Re: Permutation and Combination Help! [#permalink] New post 18 Mar 2011, 00:58
Hey thanks for the help! And I'll take note of that, Entwistle.

However the answer is supposed to be 207. /: I finally figured out the solution, but it doesn't make sense! I used your method to tackle this question as well.

Soln: No. of committees= 10C4-4C3=207
Senior Manager
Senior Manager
Joined: 23 Jun 2009
Posts: 361
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Followers: 5

Kudos [?]: 93 [0], given: 60

GMAT Tests User
Re: Permutation and Combination Help! [#permalink] New post 18 Mar 2011, 07:08
4 people can be chosen from 10 people in 10C4 = 210 ways. Question only wants us to exclude the last case, 2 couples are in commitee. That is 3C2=3 possibilities.
210-3=207
GMAT Pill Instructor
User avatar
Joined: 14 Apr 2009
Posts: 1367
Location: New York, NY
Followers: 257

Kudos [?]: 553 [0], given: 5

Re: Permutation and Combination Help! [#permalink] New post 18 Mar 2011, 08:14
Expert's post
Ah--in that case, the question relies on a critical assumption: that couples don't necessarily stay together.

The analysis above assumes that couples stay together.

But if couples do not stay together, then a lot more possibilities exist:

You can have 1 married person, and 3 singles.
You can have 2 married people, and 2 singles.
You can have 3 married people, and 1 single.
You can have 4 married people (only 2 of them can be a couple, the other 2 cannot).

So this complicates things further. In this case, using the method maliyeci and yogibearsayshi suggested above, you find the total possible combinations and then subtract the 1 case scenario that is prohibited.

So you treat the married people like singles in terms of calculations, but then subtract out the case when there are 2 married couples.

So yes, that would be 10C4 - 3C2.
10C4 because you are selecting from 10 and choosing 4 people (regardless of married/single status).
3C2 because you want the # of people possibilities for 2 married couples that you want to subtract from the overall.

This would give you:
10C4 = 10! / (4! * 6!) = (10*9*8*7) / (4*3*2*1) = (10*3*7) / (1) = 210

3C2 = 3! / (2! * 1*) = 3

210 - 3 = 207

I'm not so sure you'd see a question worded like this on the actual GMAT. The calculation with the factorials is a little bit more in depth than I would expect. But good to go through though.
_________________


... and more


Image What's Inside GMAT Pill?

Zeke Lee, GMAT Pill Study Method (Study Less. Score More.)


GMAT Pill Reviews | GMAT PILL Free Practice Test

Senior Manager
Senior Manager
User avatar
Joined: 05 Jul 2010
Posts: 359
Followers: 15

Kudos [?]: 39 [0], given: 17

GMAT ToolKit User GMAT Tests User
Re: Permutation and Combination Help! [#permalink] New post 19 Mar 2011, 11:38
I 100% DON'T agree with GMAT Pill Instructor initial assumption!! No where in the question it says you can assume married couple don't split up.

*Here is the solution in simple terms:*
1. All 4 single = 4C4 = 1
2. 1 married couple included = 3C1* (for the rest 2 there are 3 cases: 2 are single + 1 is married*1 is single + 2 are married)
= 3C1* ( 4C2 + (2C1*2)*4C1 + (2C2*2*2) )
= 3 * (6 + 16 + 4) = 3 * 26 = 78
3. 1 married & 3 single = (3C1*2)*4C3 = 24
4. 2 married & 2 single = (3C2*2*2)*4C2 = 12*6=72
5. 3 married & 1 single = (3C3*2*2*2)*4C1 = 8*4=32

Total = 1+ 78 + 24 + 72 + 32 = 207

I might have done some calculation mistake (forgive me for that), but hope you got the point.

*Alternative approach:* (I always thing of negative approach as if you go to harder levels, GMAT I think likes to test this way of your thinking)
At-most 1 married couple
= Total possible ways - 2 married couple
= 10C4 - 3C2
= 210 - 3
= 207

Hope this helps!
Director
Director
Status: -=GMAT Jedi=-
Joined: 04 Jan 2011
Posts: 741
Location: Kochi, India
Schools: ISB
WE 1: Engineer - Larsen & Toubro, ECC Division
WE 2: Faculty - T.I.M.E.
Followers: 29

Kudos [?]: 116 [0], given: 66

GMAT Tests User
Re: Permutation and Combination Help! [#permalink] New post 19 Mar 2011, 16:01
Damn :x

Stupid me for not reading the problem properly :|

Thank you gmatpill!
_________________

Mission: Be a force of good and make a positive difference to every life I touch!

From 650 to 710 to 750 - My Tryst With GMAT [Experience Thread]

Director
Director
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 934
Followers: 11

Kudos [?]: 165 [0], given: 123

Reviews Badge
Re: Permutation and Combination Help! [#permalink] New post 21 Mar 2011, 12:18
Pls move this to PS Quant forum.
Intern
Intern
Joined: 30 Mar 2011
Posts: 48
Schools: Virginia Tech
Followers: 0

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

Re: Permutation and Combination Help! [#permalink] New post 01 Apr 2011, 14:51
Typically, how many P&C questions will you encounter?
GMAT Pill Instructor
User avatar
Joined: 14 Apr 2009
Posts: 1367
Location: New York, NY
Followers: 257

Kudos [?]: 553 [0], given: 5

Re: Permutation and Combination Help! [#permalink] New post 04 Apr 2011, 09:11
Expert's post
aznboi986 wrote:
Typically, how many P&C questions will you encounter?


Well, the test is adaptive. P&C questions are usually tougher so if you don't answer enough hard questions to get here, then you might not encounter any. However, if you are looking to score in the 700 range, you will likely encounter a few (2 or 3) in varying difficulties. Often times you can think through the variations, but understanding the formula as well as Permutations vs combinations vs variations will help you answer the question quickly and accurately without having a panic during exam time.
_________________


... and more


Image What's Inside GMAT Pill?

Zeke Lee, GMAT Pill Study Method (Study Less. Score More.)


GMAT Pill Reviews | GMAT PILL Free Practice Test

Re: Permutation and Combination Help!   [#permalink] 04 Apr 2011, 09:11
    Similar topics Author Replies Last post
Similar
Topics:
Popular new posts 11 Experts publish their posts in the topic Permutations & Combinations : Help is on the way! conalcharles 24 13 Oct 2004, 21:53
Popular new posts 4 COMBINATION PERMUTATION QUESTION HELP!! lucalelli88 18 14 Jan 2010, 02:55
New posts Experts publish their posts in the topic Permutation and Combination Help anuu 2 22 Apr 2011, 09:14
New posts Very Helpful Review on Permutations and Combinations shs0145 0 09 Jun 2011, 09:16
Display posts from previous: Sort by

Permutation and Combination Help!

  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®.