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

It is currently 02 Sep 2014, 03:49

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

How many different ways to play doubles tennis ?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
User avatar
Joined: 29 Jun 2010
Posts: 251
Schools: LBS, Oxford
Followers: 8

Kudos [?]: 22 [0], given: 12

GMAT Tests User
How many different ways to play doubles tennis ? [#permalink] New post 12 Jul 2011, 01:20
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

30% (01:14) correct 70% (05:28) wrong based on 10 sessions
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?

A. 420
B. 2520
C. 168
D. 90
E. 105
[Reveal] Spoiler: OA
2 KUDOS received
Current Student
avatar
Joined: 26 May 2005
Posts: 571
Followers: 18

Kudos [?]: 108 [2] , given: 13

GMAT Tests User
Re: How many different ways to play doubles tennis ? [#permalink] New post 12 Jul 2011, 01:26
2
This post received
KUDOS
Alchemist1320 wrote:
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?

A. 420
B. 2520
C. 168
D. 90
E. 105


Formula = 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 important is (mn)!/n^m*m!

so its 8!/(2^4*4!) = 105 = E
Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4699
Location: Pune, India
Followers: 1091

Kudos [?]: 4890 [2] , given: 163

Re: How many different ways to play doubles tennis ? [#permalink] New post 12 Jul 2011, 02:42
2
This post received
KUDOS
Expert's post
Alchemist1320 wrote:
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?

A. 420
B. 2520
C. 168
D. 90
E. 105


From the question, we can say that the teams are not distinct i.e. we don't have team A, team B etc. But let's solve this question by making first team, second team, third team and fourth team. Later we will adjust the answer.
Out of 8 people, how can you make the first team? In 8C2 ways.
Out of 6 people, how can you make the second team? In 6C2 ways.
Out of 4 people, how can you make the third team? In 4C2 ways.
Out of 2 people, how can you make the fourth team? In 2C2 ways.
How can you make the 4 teams?
8C2 *6C2*4C2*2C2

But here, we have considered the 4 teams to be distinct. We called them 'first team', 'second team' etc.
So we need to divide the result by 4! to 'un-arrange' them.

You get: 8C2 *6C2*4C2*2C2/4! = 8*7*6*5*4*3*2*1/16*4! = 105
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Manager
avatar
Joined: 14 Feb 2011
Posts: 70
Followers: 1

Kudos [?]: 1 [0], given: 2

GMAT ToolKit User
Re: How many different ways to play doubles tennis ? [#permalink] New post 08 Aug 2011, 06:16
sudhir18n wrote:
Alchemist1320 wrote:
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?

A. 420
B. 2520
C. 168
D. 90
E. 105


Formula = 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 important is (mn)!/n^m*m!

so its 8!/(2^4*4!) = 105 = E


super! thanks for formula!
Manager
Manager
avatar
Status: Do till 740 :)
Joined: 13 Jun 2011
Posts: 104
Concentration: Strategy, General Management
GMAT 1: 460 Q35 V20
GPA: 3.6
WE: Consulting (Computer Software)
Followers: 0

Kudos [?]: 5 [0], given: 18

GMAT ToolKit User
Re: How many different ways to play doubles tennis ? [#permalink] New post 14 Sep 2011, 13:20
karishma,

Quote:
But here, we have considered the 4 teams to be distinct. We called them 'first team', 'second team' etc.
So we need to divide the result by 4! to 'un-arrange' them.



Can you please explain this?
I understand that we divide the slots! to remove identical stuff but here how does it make sense?
Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4699
Location: Pune, India
Followers: 1091

Kudos [?]: 4890 [2] , given: 163

Re: How many different ways to play doubles tennis ? [#permalink] New post 14 Sep 2011, 21:07
2
This post received
KUDOS
Expert's post
shankar245 wrote:
Can you please explain this?
I understand that we divide the slots! to remove identical stuff but here how does it make sense?


This is the logic behind this step:

Say there are 4 boys: A, B, C, D
There are two ways of splitting them in two groups.

Method I

The two groups can be made in the following ways
1. AB and CD
2. AC and BD
3. AD and BC

The groups are not named/distinct. You have 4 boys in front of you and you split them in 2 groups and do not name the groups. There are 3 total ways of doing this.

Method II
On the other hand, I could put them in two distinct groups in the following ways
1. Group1: AB, Group2: CD
2. Group1: CD, Group2: AB (If you notice, this is the same as above, just that now AB is group 2)
3. Group1: AC, Group2: BD
4. Group1: BD, Group2: AC
5. Group1: AD, Group2: BC
6. Group1: BC, Group2: AD

Here I have to put them in two different groups, group 1 and group 2. AB and CD is not just one way of splitting them. AB could be assigned to group 1 or group 2 so there are 2 cases. In this case, every 'way' we get above will have two possibilities so total number of ways will be twice.
So there will be 6 total ways.

Here since the groups are not distinct but 8C2 * 6C2 * 4C2 * 2C2 makes them distinct (we say, select the FIRST group in 8C2 ways, SECOND group in 6C2 ways etc), we need to divide by 4!.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Manager
avatar
Status: Do till 740 :)
Joined: 13 Jun 2011
Posts: 104
Concentration: Strategy, General Management
GMAT 1: 460 Q35 V20
GPA: 3.6
WE: Consulting (Computer Software)
Followers: 0

Kudos [?]: 5 [0], given: 18

GMAT ToolKit User
Re: How many different ways to play doubles tennis ? [#permalink] New post 14 Sep 2011, 21:41
thanks karishma for that detailed explanation :)
Manager
Manager
avatar
Joined: 06 Feb 2011
Posts: 84
GMAT 1: Q V
GMAT 2: Q V
GMAT 3: Q V
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 8 [0], given: 11

GMAT Tests User
Re: How many different ways to play doubles tennis ? [#permalink] New post 15 Sep 2011, 07:57
Thanks Sudhir , I did not (know) the formula .. and was coming up with 8C2 + 6C2+ 4C2 + 2C2 which is obviously wrong. After I read the formula, it came back to me from school days!!

Thanks Karishma, for the detailed explanation it was really helpful.
Re: How many different ways to play doubles tennis ?   [#permalink] 15 Sep 2011, 07:57
    Similar topics Author Replies Last post
Similar
Topics:
1 A group of 8 friends want to play doubles tennis. How many namurad 7 17 Jun 2008, 08:10
Experts publish their posts in the topic A group of 8 friends wants to play double tennis. How many puma 8 08 Jun 2008, 11:03
28 Experts publish their posts in the topic A group of 8 friends want to play doubles tennis. How many Balvinder 26 10 Nov 2007, 20:43
A group of 8 friends want to play doubles tennis. How many mophead 6 02 Nov 2005, 02:38
3 A group of 8 friends want to play doubles tennis. How many GMATT73 28 02 Oct 2005, 01:51
Display posts from previous: Sort by

How many different ways to play doubles tennis ?

  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®.