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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Re: Permutation and Combination Help! [#permalink]

Show Tags

17 Mar 2011, 14:56

1

This post received KUDOS

Expert's post

3

This post was BOOKMARKED

Hi yogibearsayshi,

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

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.

Re: Permutation and Combination Help! [#permalink]

Show Tags

18 Mar 2011, 01:58

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.

Re: Permutation and Combination Help! [#permalink]

Show Tags

18 Mar 2011, 08:08

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

Re: Permutation and Combination Help! [#permalink]

Show Tags

18 Mar 2011, 09:14

1

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

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. _________________

Re: Permutation and Combination Help! [#permalink]

Show Tags

19 Mar 2011, 12:38

1

This post received KUDOS

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

Re: Permutation and Combination Help! [#permalink]

Show Tags

04 Apr 2011, 10:11

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. _________________

Re: Permutation and Combination Help! [#permalink]

Show Tags

27 Jun 2014, 16:11

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. _________________

Re: Permutation and Combination Help! [#permalink]

Show Tags

29 Sep 2015, 12:18

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. _________________

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

Cal Newport is a computer science professor at GeorgeTown University, author, blogger and is obsessed with productivity. He writes on this topic in his popular Study Hacks blog. I was...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...