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

It is currently 25 Oct 2014, 22:30

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

A Coach is filling out the starting lineup for his indoor

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 24 Mar 2010
Posts: 81
Followers: 0

Kudos [?]: 21 [0], given: 134

Re: Combination or Permutation: Can't make up my mind :) [#permalink] New post 24 Dec 2012, 01:06
144144 wrote:
i made the same mistake as rvthryet... thanks for the explanation even tho i still dont understand how it makes such a different. i can c from your example that it happens. but i cannot understand the logic behind it. at the end he is choosing 5 ppl out of 8. the order have no effect.

but from what u are saying - unless its very clear that i need to choose only 5 ppl from a group without ANY distinction - it will be 5C8...

thanks bunuel.


With the 8C5 logic, you are not accommodating the case where 2 defenders are different from 2 midfielders.

To pick up on the 4 player example Bunuel gave, 4 players - A,B,C,D we should choose 1 for defense and 1 for forward. (no restrictions).

When we do 4C2
Defence-forward
AB
AC
AD
BC
BD
CD


But we are missing the case CA where C is defender and A is forward. In this particular example we can use the nPr permutation formula.

Back to original question, Bunuels method is pretty kickass.
_________________

- Stay Hungry, stay Foolish -

Intern
Intern
avatar
Joined: 19 Nov 2012
Posts: 43
Concentration: Marketing, Strategy
GMAT 1: 750 Q47 V47
Followers: 0

Kudos [?]: 8 [0], given: 4

Re: A Coach is filling out the starting lineup for his indoor [#permalink] New post 25 Oct 2013, 09:29
I arrived at D as well.

Quick question:

Obviously, the order is important here, which is why we do not account for repetitions.

How would the wording of the question change if order did not matter, which would lead us to divide D by n!?
Current Student
avatar
Joined: 12 Dec 2012
Posts: 34
Concentration: Leadership, Social Entrepreneurship
GMAT 1: Q V
GMAT 2: 660 Q48 V33
GMAT 3: 740 Q49 V41
GPA: 3.74
Followers: 2

Kudos [?]: 48 [0], given: 19

Re: Combination or Permutation: Can't make up my mind :) [#permalink] New post 06 Nov 2013, 23:00
Bunuel wrote:
rvthryet wrote:
Small doubt.. Why should this not be 2C1 x 8C5??

I just can't seem to understand how is my thinking flawed there, although it is quite obvious that it is :oops:


Imagen different situation 4 players, we should choose 1 for defense and 1 for forward. (no restrictions).

The way you are doing you'll get 4C2=6. But look at the real case.

ABCD (players):

Defence - Forward
A B
A C
A D

B A
B C
B D

C A
C B
C D

D A
D B
D C

Total 12 possibilities 4C1*3C1=4*3=12. You just narrowed possible ways of selection.

In original question we are not choosing 5 people from 8, but we are choosing 2 from 8, than 2 from 6, than 1 from 4 (well and before we chose 1 from 2 as goalkeeper). And this is more ways of selection than 8C5 as you can see in the example.


Bunuel - I see how you arrived at D, but initially when I solved this problem I adjusted it because the order in which we make these selections shouldn't matter. Right?

We are making a team of 6 - so we need to select : 1GK (2C1), 2 Midfielders (8C2), 2 Defenders (6C2), 1 Forward (4C1) = 3360 (but aren't we over counting here, since it doesn't matter what order we make these selections in? So shouldn't we divide this by 4! to give us 140 different groupings?

I made the mistake of NOT doing this on previous 'different grouping' questions and find it quite confusing. If you can explain when do adjust / when not to, it would be helpful!

Cheers
Intern
Intern
avatar
Joined: 01 May 2013
Posts: 1
Schools: Stanford '16
GMAT 1: 760 Q50 V44
Followers: 0

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

Re: A Coach is filling out the starting lineup for his indoor [#permalink] New post 16 Nov 2013, 07:34
You can alternatively come to the same conclusion using another approach:

First part - main team. There are 8 options (10 teammates excluding 2 goalkeepers). It means 8! combinations. But there are repeating elements. 2 defenders - that is 2!, 2 midfield - 2!, and 3 will not be chosen and order inside of this unlucky team is also irrelevant, thereby 3!.

So we've got: 8! / (2!*2!*3!)

Second part is pretty easier - goalkeepers. There are two of them, one is to be chosen - 2 options.

Now we have: 2*8! / (2!*2!*3!)
Intern
Intern
avatar
Joined: 10 Dec 2013
Posts: 19
Location: India
Concentration: Technology, Strategy
Schools: ISB '16 (S)
GMAT 1: 710 Q48 V38
GPA: 3.9
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 6 [0], given: 7

Re: A Coach is filling out the starting lineup for his indoor [#permalink] New post 28 Jan 2014, 10:40
Why cant we solve this by simple number theory?? If we use that approach then the answer changes
first we will have the 2 goalies, then 8 choices for first defender, then 7 choices for second defender and so on and so forth.
This would give us the answer as 2*8*7*6*5*4 = 13440

I know this is wrong answer but can someone please help me understand why this approach is wrong. Just because we are considering each position at a time?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23422
Followers: 3619

Kudos [?]: 28988 [0], given: 2874

Re: A Coach is filling out the starting lineup for his indoor [#permalink] New post 29 Jan 2014, 07:45
Expert's post
Rohan_Kanungo wrote:
Why cant we solve this by simple number theory?? If we use that approach then the answer changes
first we will have the 2 goalies, then 8 choices for first defender, then 7 choices for second defender and so on and so forth.
This would give us the answer as 2*(8*7)*(6*5)*4 = 13440

I know this is wrong answer but can someone please help me understand why this approach is wrong. Just because we are considering each position at a time?


The point is that the number of ways to select 2 out of 8 is NOT 8*7=56 it's C^2_8=28 and the number of ways to select 2 out of 6 is NOT 6*5=30 it's C^2_6=15.

Hope it's clear.
_________________

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

Manager
Manager
avatar
Joined: 14 Nov 2011
Posts: 147
Location: United States
Concentration: General Management, Entrepreneurship
Schools: Stanford '15
GPA: 3.61
WE: Consulting (Manufacturing)
Followers: 0

Kudos [?]: 17 [0], given: 97

GMAT ToolKit User
Re: A Coach is filling out the starting lineup for his indoor [#permalink] New post 09 Jun 2014, 06:48
Bunuel wrote:
Rohan_Kanungo wrote:
Why cant we solve this by simple number theory?? If we use that approach then the answer changes
first we will have the 2 goalies, then 8 choices for first defender, then 7 choices for second defender and so on and so forth.
This would give us the answer as 2*(8*7)*(6*5)*4 = 13440

I know this is wrong answer but can someone please help me understand why this approach is wrong. Just because we are considering each position at a time?


The point is that the number of ways to select 2 out of 8 is NOT 8*7=56 it's C^2_8=28 and the number of ways to select 2 out of 6 is NOT 6*5=30 it's C^2_6=15.

Hope it's clear.



Hi Bunnel,

In this question why we not dividing by 3! ?

2c1 * {(8c2*6c2*4c1)/3!}

and why do we do so in the below question?

The Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is available in four colors: blue, black, red, and green. How many different combinations of three cars can the Carsons select if all the cars are to be different colors?

a) 24
b) 32
c) 48
d) 60
e) 192
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23422
Followers: 3619

Kudos [?]: 28988 [0], given: 2874

Re: A Coach is filling out the starting lineup for his indoor [#permalink] New post 09 Jun 2014, 08:20
Expert's post
cumulonimbus wrote:
Bunuel wrote:
Rohan_Kanungo wrote:
Why cant we solve this by simple number theory?? If we use that approach then the answer changes
first we will have the 2 goalies, then 8 choices for first defender, then 7 choices for second defender and so on and so forth.
This would give us the answer as 2*(8*7)*(6*5)*4 = 13440

I know this is wrong answer but can someone please help me understand why this approach is wrong. Just because we are considering each position at a time?


The point is that the number of ways to select 2 out of 8 is NOT 8*7=56 it's C^2_8=28 and the number of ways to select 2 out of 6 is NOT 6*5=30 it's C^2_6=15.

Hope it's clear.



Hi Bunnel,

In this question why we not dividing by 3! ?

2c1 * {(8c2*6c2*4c1)/3!}

and why do we do so in the below question?

The Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is available in four colors: blue, black, red, and green. How many different combinations of three cars can the Carsons select if all the cars are to be different colors?

a) 24
b) 32
c) 48
d) 60
e) 192


Because for this case the order of the selection matters: A = defense, B = midfield, C = forward is different from B = defense, A = midfield, C = forward, ... Therefore here we don't need factorial correction. While for "Carson family" problem Blue A/Black A/Red A is the same as Black A/Red A/Blue A...

Hope it's clear.

P.S. You can solve the second question with another approach described here: the-carson-family-will-purchase-three-used-cars-there-are-128876.html#p1056566
_________________

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

Manager
Manager
avatar
Joined: 30 Mar 2013
Posts: 86
Followers: 0

Kudos [?]: 12 [0], given: 135

Re: A Coach is filling out the starting lineup for his indoor [#permalink] New post 23 Sep 2014, 07:42
amkabdul wrote:
Guys... since we have 6 positions in the field which are to be filled with 10 players.

Look at this: Filling the goal keeper position in 2 ways.
Next: the rest of the 5 positions are to be filled with 8 players and each player at a different position would be 8p5 But since we have 2 positions each for the defence and mid. divide it with 2! twice.

So answer is : 2* (8P5/(2!*2!)) = 3360

A very simple and easy approach based on the basics of P 'n C

Kudo me if you like this.


Agreed about the permutations approach. I was under the impression that we use permutations when there are places specified in the group, as there are here. I dont understand the combinations approach at all. For eg, in how many ways can you select a president and VP from a group of 6. Should be 6*5=30, or 6P2= 30.

Can someone please point me in the direction where I can understand when to apply C and when to apply P. I understand that P is applied when order is imp, but the problem is, that when selecting president and VP from a group, order shouldn't be important. AB or BA is the same, and therefore, even those should be solved by using combinations. I hope I'm explaining my confusion well enough for someone to help me :oops:
Re: A Coach is filling out the starting lineup for his indoor   [#permalink] 23 Sep 2014, 07:42
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic Jim filled his dog's bowl with 80 dog food pellets. Starting gmatquant25 2 25 May 2014, 14:01
3 Although the batting coach conceded the new lineup, in which mbaMission 16 09 Jun 2009, 07:23
7 Experts publish their posts in the topic Coach Miller is filling out the starting lineup for his jimjohn 18 25 Dec 2007, 15:44
Coach Miller is filling out the starting lineup for his Zem 8 09 Apr 2005, 00:19
Coach Miller is filling out the starting lineup for his gayathri 9 17 Jan 2005, 13:40
Display posts from previous: Sort by

A Coach is filling out the starting lineup for his indoor

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page   Previous    1   2   [ 29 posts ] 



cron

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®.