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:

Re: combination (groups and that stuff...) [#permalink]

Show Tags

24 Oct 2009, 18:50

8

This post received KUDOS

Expert's post

8

This post was BOOKMARKED

The answer to the question is 105, not 2520. I posted a solution on another forum, which I'll paste here:

________

Think of this question:

A group of eight tennis players will be divided into four teams of two. One team will play in the Olympics, one in Wimbledon, one in the Davis Cup and one in the US Open. In how many different ways can the teams be selected?

Here, the order of the teams themselves clearly matters. If we choose {A,B} to go to the Olympics, and {C,D} to go to Wimbledon, that's clearly different from sending {C,D} to the Olympics and {A,B} to Wimbledon. The answer to this question is exactly the answer you give above:

-you have 8C2 choices for the Olympics team; -you have 6C2 choices for the Wimbledon team; -you have 4C2 choices for the Davis Cup team; -you have 2C2 (one) choice for the US Open team.

Multiply these to get the answer: 8C2*6C2*4C2*2C2 = (8*7/2)(6*5/2)(4*3/2)(2*1/2) = 2520.

Note that the question I've just asked above is different from the question in the original post. In this question:

A group of 8 friends want to play doubles tennis. How many different ways can the group be divided into 4 teams of 2 people?

the order of the teams does not matter. If we choose, say, these teams:

{A,B}, {C,D}, {E,F}, {G,H}

that's exactly the same set of teams as these:

{C,D}, {A,B}, {G,H}, {E,F}

Because the order of the teams themselves does not matter, we must divide by 4! = 24, the number of different orders we can put the four teams in, because all 24 different orders are in fact the same set of teams. So the answer is 2520/4! = 105. _________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Re: combination (groups and that stuff...) [#permalink]

Show Tags

24 Oct 2009, 18:56

12

This post received KUDOS

Expert's post

6

This post was BOOKMARKED

I think there is a little problem with the solutions above:

Does the order matters? Think not. (1,2)(3,4)(5,6)(7,8) should be the same 4 teams as (5,6)(7,8)(1,2)(3,4), as we don't have team #1, team #2...

So 2520 should be divided by 4!=105.

Answer: A.

I know there is a formula to determine:

A. the number of ways in which mn different items can be divided equally into m groups, each containing n objects and the order of the groups is not important. B. the number of ways in which mn different items can be divided equally into m groups, each containing n objects and the order of the groups is important.

Basically hgp2k used here the second one, but these formulas are not needed for GMAT and there is an easier way to solve this problem, well at least I solve this way and find it easier:

For the first person we can pick a pair in 7 ways; For the second one in 5 ways (as two are already chosen); For the third one in 3 ways (as 4 people are already chosen); For the fourth one there is only one pair left.

I cannot comprehend this concept Lets say there are 4 people, ABCD to be arranged in two groups of two. There are 6 ways of doing this: AB, AC, AD, BC, BD and CD. If we use the above formula we get 4C2*2C2 / 2! = 6/2 = 3 !!! What is the difference ??!!??

I was struggling with the question as well and wanted to use similar logic. Here's my thought - the question asks In how many different ways can a group of 8 people be divided into 4 teams of 2 people each?

Which, IMO, is slightly different from "How many teams of two can we create from a group of 8 people?" The first question assumes that one string of teams is one unit.

Using the example above,

AB CD AC BD AD BC

Gives us three units of teams (6/2!) = 3. I think it's just a different way of looking at it - we have 6 teams but only three possible SETS of teams - therefore, we additionally have to divide by the factor of the number of teams.

Re: In how many different ways can a group of 8 people be divide [#permalink]

Show Tags

29 Oct 2013, 03:13

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: combination (groups and that stuff...) [#permalink]

Show Tags

18 Nov 2013, 18:36

Two questions are asked; First the no of ways in which 2 can e selected fro 8 peoples; = 8C2 * 6C2 * 4C2* 2C2 =(8!/6!*2!)*(6!/4!*2!)*(4!/2!*2!)*(2!/2!*0!) =2520

Second the no of ways in which 2 can be arranged among 4 groups ; since the arrangement will vary hence simple factorial of will be the choice which is 4!

So finally you need to divide the former by later to get the answer =2520/4! =105 _________________

Re: combination (groups and that stuff...) [#permalink]

Show Tags

30 Dec 2013, 06:03

1

This post received KUDOS

IanStewart wrote:

The answer to the question is 105, not 2520. I posted a solution on another forum, which I'll paste here:

________

Think of this question:

A group of eight tennis players will be divided into four teams of two. One team will play in the Olympics, one in Wimbledon, one in the Davis Cup and one in the US Open. In how many different ways can the teams be selected?

Here, the order of the teams themselves clearly matters. If we choose {A,B} to go to the Olympics, and {C,D} to go to Wimbledon, that's clearly different from sending {C,D} to the Olympics and {A,B} to Wimbledon. The answer to this question is exactly the answer you give above:

-you have 8C2 choices for the Olympics team; -you have 6C2 choices for the Wimbledon team; -you have 4C2 choices for the Davis Cup team; -you have 2C2 (one) choice for the US Open team.

Multiply these to get the answer: 8C2*6C2*4C2*2C2 = (8*7/2)(6*5/2)(4*3/2)(2*1/2) = 2520.

Note that the question I've just asked above is different from the question in the original post. In this question:

A group of 8 friends want to play doubles tennis. How many different ways can the group be divided into 4 teams of 2 people?

the order of the teams does not matter. If we choose, say, these teams:

{A,B}, {C,D}, {E,F}, {G,H}

that's exactly the same set of teams as these:

{C,D}, {A,B}, {G,H}, {E,F}

Because the order of the teams themselves does not matter, we must divide by 4! = 24, the number of different orders we can put the four teams in, because all 24 different orders are in fact the same set of teams. So the answer is 2520/4! = 105.

This is great to clarify Ian

So basically we have three levels among permutations and combinations we have:

Permutation where order of elements does matter for instance {A,B,C} is different from {B,C,A} and so on Then we have combinations in which order does not matter in these cases {A,B,C} = {C,B,A}, but if we have two groups then say group 1 is {A,B,C} and group 2 is {D,E,F} then {1,2} is different from {2,1}, as you explained in your example with the tennis couples going to different tournaments. So the order of the sets themselves ARE important.

Now if we DON'T care about the order of the arrangements of the SETS (not the elements within the sets), then we get to our third level in which we need to divide by n! (n being the number of GROUPS) so that we are stating no preference over order of sets.

Re: In how many different ways can a group of 8 people be divide [#permalink]

Show Tags

03 Apr 2015, 18:22

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: In how many different ways can a group of 8 people be divide [#permalink]

Show Tags

10 Apr 2016, 22:39

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. _________________

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...

They say you get better at doing something by doing it. then doing it again ... and again ... and again, and you keep doing it until one day you look...

I barely remember taking decent rest in the last 60 hours. It’s been relentless with submissions, birthday celebration, exams, vacating the flat, meeting people before leaving and of...