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:

Given that there are 6 married couples. If we select only 4 people out of the 12, what is the probability that none of them are married to each other?

total ways of choosing 4 out of 12:12x11x10x9 first person can be chosen in 12 ways. The next person can be chosen in 10 ways (because we don't want spouses to be in the group). The next person can be again chosen in only 8 ways (out of the 10 people left, we have to exclude 2 whose spouses we have already selected). And the last person in 6 ways.

Re: Given that there are 6 married couples. If we select only 4 [#permalink]
16 Dec 2011, 12:11

Hey please suggest where I am going wrong.

probability that none of the couple is on the group is = 1-(probability that exactly 1 couple is there) - (probability that 2 couples are there

probability of 1 couple being there : of the 6 couples an 1 can be selected in 6C1 = 6 ways . the third person can be chosen in 10 ways (leaving out the couple selected). the 4th person can be selected in 8 ways (leaving out the couple selected, the 3rd person selected and the spouse of the 3rd person selected) = 6*10*8 = 480 ways.. since total number of ways = 12C4. therefore probability that 1 couple is part of teh selection is 480/12C4

probability of both couple being there = 6C2/12C4.

therefore probability that no couple is there : 1- [(480/12C4)+(6C2/12C4)] = 1/2

Please tell me what is wrong with this method.. Many Thanks

Re: Given that there are 6 married couples. If we select only 4 [#permalink]
08 Dec 2013, 08:53

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. _________________

\(\frac{10}{11}\) - we choose 10=12-1(prevous choice)-1(another people out of couple) of 11=12-1(prevous choice).

\(\frac{8}{10}\) - we choose 8=12-2(prevous choice)-2(another people out of couple) of 10=12-2(prevous choice).

\(\frac{6}{9}\) - we choose 6=12-3(prevous choice)-3(another people out of couple) of 9=12-3(prevous choice). _______________________

\(p=\frac{P^6_4*(P^2_1)^4}{P^{12}_4}=\frac{16}{33}\) the same logic as for \(C_m^n\)

The Question was "Given that there are 6 married couples. If we select only 4 people out of the 12, what is the probability that none of them are married to each other?"

I am not able to understand why "\(\frac{12}{12}\) - we choose 12 of 12."

Shouldn't this be 1/12 because the first person can be any 1 of the 12......There is something I am missing.....

Math Gurus: Your inputs please _________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

\(\frac{10}{11}\) - we choose 10=12-1(prevous choice)-1(another people out of couple) of 11=12-1(prevous choice).

\(\frac{8}{10}\) - we choose 8=12-2(prevous choice)-2(another people out of couple) of 10=12-2(prevous choice).

\(\frac{6}{9}\) - we choose 6=12-3(prevous choice)-3(another people out of couple) of 9=12-3(prevous choice). _______________________

\(p=\frac{P^6_4*(P^2_1)^4}{P^{12}_4}=\frac{16}{33}\) the same logic as for \(C_m^n\)

The Question was "Given that there are 6 married couples. If we select only 4 people out of the 12, what is the probability that none of them are married to each other?"

I am not able to understand why "\(\frac{12}{12}\) - we choose 12 of 12."

Shouldn't this be 1/12 because the first person can be any 1 of the 12......There is something I am missing.....

Math Gurus: Your inputs please

12/12=1 is another way of saying: choosing ANY for the first person (probability of 1). _________________

Hi -- can someone please explain the reasoning for the last two equations? In the second equation, it stating the different ways 4 couples out of six can be selected(to give 4 individual people), followed by how many different ways to select 1 person out of the 2 people in a couple(and do it 4 times) and follow that by dividing the whole quantity by 12C4. Can you explain WHY you're doing this?

Same with the third equation -- what's different here now that we have 4P6 and not 6C4?

An additional question -- I've seen the equation (12C1 * 10C1 * 8C1*6C1)/4!/ 12C4 -- why do we divide by 4! instead of multiply by 4!?

Re: Given that there are 6 married couples. If we select only 4 [#permalink]
28 Aug 2015, 01:52

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. _________________

Can you tell me why there is no difference between the results of combination and permutation formula. Hope I am not asking something odd. _________________

Freedom is not a gift...It is a responsibility to pass on.....

gmatclubot

Re: Given that there are 6 married couples. If we select only 4
[#permalink]
24 Sep 2015, 06:43

Low GPA MBA Acceptance Rate Analysis Many applicants worry about applying to business school if they have a low GPA. I analyzed the low GPA MBA acceptance rate at...

http://blog.davidbbaker.com/wp-content/uploads/2015/11/12249800_10153820891439090_8007573611012789132_n.jpg When you think about an MBA program, usually the last thing you think of is professional collegiate sport. (Yes American’s I’m going...

Every student has a predefined notion about a MBA degree:- hefty packages, good job opportunities, improvement in position and salaries but how many really know the journey of becoming...