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

It is currently 22 Jul 2014, 23:54

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

In how many different ways can a group of 8 people be

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 14 Apr 2010
Posts: 230
Followers: 2

Kudos [?]: 18 [0], given: 1

GMAT Tests User
In how many different ways can a group of 8 people be [#permalink] New post 13 Aug 2010, 07:38
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

46% (01:45) correct 54% (01:16) wrong based on 113 sessions
In how many different ways can a group of 8 people be divided into 4 teams of 2 people each?

A. 90
B. 105
C. 168
D. 420
E. 2520
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Feb 2012, 14:05, edited 2 times in total.
Edited the question and added the OA
Expert Post
7 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18684
Followers: 3233

Kudos [?]: 22230 [7] , given: 2601

Re: ways to divide?? [#permalink] New post 13 Aug 2010, 07:59
7
This post received
KUDOS
Expert's post
bibha wrote:
In how many different ways can a group of 8 people be divided into 4 teams of 2 people each?
90
105
168
420
2520


\frac{C^2_8*C^2_6*C^2_4*C^2_2}{4!}=105, we are dividing by 4! (factorial of the # of teams) as the order of the teams does not matter. If 8 people are - 1, 2, 3, 4, 5, 6, 7, 8, then (1,2)(3,4)(5,6)(7,8) would be the same 4 teams as (5,6)(7,8)(1,2)(3,4), as we don't have team #1, team #2...

You can think about this in another way.
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 left.

So we have 7*5*3*1=105

Answer: B.

You can check similar problems:
probability-88685.html?hilit=different%20items%20divided%20equally
probability-85993.html?highlight=divide+groups
combination-55369.html#p690842
sub-committee-86346.html?highlight=divide+groups


There is also direct formula for this:

1. 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 is \frac{(mn)!}{(n!)^m*m!}.

2. 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 is \frac{(mn)!}{(n!)^m}

Hope it helps.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 19 Mar 2012
Posts: 10
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: In how many different ways can a group of 8 people be [#permalink] New post 24 Mar 2012, 11:13
Another way to think about this:

How many ways can you arrange the following:
T1 T1 T2 T2 T3 T3 T4 T4

That would be: 8!/(2!*2!*2!*2!)

Then also recall that we don't care about the differences between the teams, therefore

8!/(2!*2!*2!*2!*4!) = 105
Intern
Intern
avatar
Joined: 23 Aug 2012
Posts: 13
Followers: 0

Kudos [?]: 1 [0], given: 8

Re: ways to divide?? [#permalink] New post 04 Sep 2012, 14:45
Bunuel wrote:
bibha wrote:
In how many different ways can a group of 8 people be divided into 4 teams of 2 people each?
90
105
168
420
2520


\frac{C^2_8*C^2_6*C^2_4*C^2_2}{4!}=105, we are dividing by 4! (factorial of the # of teams) as the order of the teams does not matter. If 8 people are - 1, 2, 3, 4, 5, 6, 7, 8, then (1,2)(3,4)(5,6)(7,8) would be the same 4 teams as (5,6)(7,8)(1,2)(3,4), as we don't have team #1, team #2...

You can think about this in another way.
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 left.

So we have 7*5*3*1=105

Answer: B.
There is also direct formula for this:

1. 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 is \frac{(mn)!}{(n!)^m*m!}.

2. 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 is \frac{(mn)!}{(n!)^m}

Hope it helps.


I understand how to get the answer, but I'm wondering why we assume that the order of the teams doesn't matter. The question just asks how many ways you can group them. When should we assume something matters or doesn't matter when the question doesn't specify? And also, just to clarify, when we do 8!/2!2!2!2!4!, we are also not worrying about the order within each team either right i.e. (a,b)=(b,a)?
1 KUDOS received
Intern
Intern
avatar
Joined: 28 Aug 2012
Posts: 48
Location: Austria
GMAT 1: 770 Q51 V42
Followers: 3

Kudos [?]: 28 [1] , given: 3

Re: In how many different ways can a group of 8 people be [#permalink] New post 04 Sep 2012, 21:35
1
This post received
KUDOS
We don't worry about the order within a team or between teams, because there is nothing in the question that would make it necessary to do so.

The question needs to give us information, why we should differentiate. For example, if those teams are given numbers to or being seated on a bench.

Or if one of the team members is the captain.

But that's not the case here.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18684
Followers: 3233

Kudos [?]: 22230 [1] , given: 2601

Re: ways to divide?? [#permalink] New post 04 Sep 2012, 23:39
1
This post received
KUDOS
Expert's post
dandarth1 wrote:
Bunuel wrote:
bibha wrote:
In how many different ways can a group of 8 people be divided into 4 teams of 2 people each?
90
105
168
420
2520


\frac{C^2_8*C^2_6*C^2_4*C^2_2}{4!}=105, we are dividing by 4! (factorial of the # of teams) as the order of the teams does not matter. If 8 people are - 1, 2, 3, 4, 5, 6, 7, 8, then (1,2)(3,4)(5,6)(7,8) would be the same 4 teams as (5,6)(7,8)(1,2)(3,4), as we don't have team #1, team #2...

You can think about this in another way.
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 left.

So we have 7*5*3*1=105

Answer: B.
There is also direct formula for this:

1. 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 is \frac{(mn)!}{(n!)^m*m!}.

2. 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 is \frac{(mn)!}{(n!)^m}

Hope it helps.


I understand how to get the answer, but I'm wondering why we assume that the order of the teams doesn't matter. The question just asks how many ways you can group them. When should we assume something matters or doesn't matter when the question doesn't specify? And also, just to clarify, when we do 8!/2!2!2!2!4!, we are also not worrying about the order within each team either right i.e. (a,b)=(b,a)?


The teams are not numbered/labeled (we don't have team #1, #2, ...), the teams are not assigned to something (for example to tournaments), ... So, the order of the teams doesn't matter.

Please check the links in my previous post for similar problems.

Hope it helps.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 1708
Followers: 162

Kudos [?]: 33 [0], given: 0

Premium Member
Re: In how many different ways can a group of 8 people be [#permalink] New post 15 Sep 2013, 02:25
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.

_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
User avatar
Joined: 19 Apr 2013
Posts: 27
Concentration: Strategy, Entrepreneurship
GPA: 4
Followers: 0

Kudos [?]: 1 [0], given: 7

CAT Tests
Re: In how many different ways can a group of 8 people be [#permalink] New post 05 Jun 2014, 08:35
Bunuel, do we multiply them because of line method? Sorry for stupid question)
Re: In how many different ways can a group of 8 people be   [#permalink] 05 Jun 2014, 08:35
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic In how many different ways can a group of 8 people be manalq8 10 12 Jan 2012, 06:59
16 Experts publish their posts in the topic In how many different ways can a group of 8 people be divide noboru 15 24 Oct 2009, 03:20
In how many different ways can a group of 8 be divided into suntaurian 1 09 Mar 2008, 00:02
In how many different ways can a group of 8 be divided into Ozmba 7 09 Nov 2007, 10:49
How many different ways can a group of 8 be divided into 4 21stCenturion 6 22 Jan 2006, 08:48
Display posts from previous: Sort by

In how many different ways can a group of 8 people be

  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®.