NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 20:57 It is currently 23 Apr 2024, 20:57
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Coach Miller is filling out the starting lineup for his indoor soccer

SORT BY:
Date
Kudos
 1   2   
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
jimjohn
Manager
Manager
Joined: 19 Aug 2007
Posts: 111
Own Kudos [?]: 224 [53]
Given Kudos: 0
Send PM
Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   Updated on: 29 Apr 2019, 22:42
4
Kudos
49
Bookmarks
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

65% (02:39) correct 35% (02:57) wrong based on 818 sessions
Hide Show timer Statistics
Coach Miller is filling out the starting lineup for his indoor soccer team. There are 10 boys on th team, and he must assign 6 starters to the following positions: 1 goalkeeper, 2 on defense, 2 in midfield, and 1 forward. Only 2 of the boys can play goalkeeper, and they cannot play any other positions. The other boys can each play any of the other positions. How many different groupings are possible?

A. 60
B. 210
C. 2580
D. 3360
E. 151200
ShowHide Answer
Official Answer
D

Originally posted by jimjohn on 25 Dec 2007, 16:44.
Last edited by Bunuel on 29 Apr 2019, 22:42, edited 3 times in total.
Renamed the topic and edited the question.
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618619 [16]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   25 Oct 2009, 18:08
9
Kudos
7
Bookmarks
Expert Reply
rvthryet wrote:
A Coach is filling out the starting lineup for his indoor soccer team. There are 10 boys on the team, and he must assign 6 starters to the following positions: 1 goalkeeper, 2 on defence, 2 in midfield, and 1 forward. Only 2 of the boys can play goalkeeper, and they cannot play any other positions. The other boys can each play any of the other positions. How many different groupings are possible?

A) 60

B) 210

C) 2580

D) 3360

E) 151200


2C1 select 1 goalkeeper from 2 boys;
8C2 select 2 defense from 8 boys (as 2 boys can only play goalkeeper 10-2=8);
6C2 select 2 midfield from 6 boys (as 2 boys can only play goalkeeper and 2 we've already selected for defense 10-2-2=6);
4C1 select 1 forward from 4 boys (again as 2 boys can play only goalkeeper, 4 we've already selected for defense and midfield 10-2-4=4)

Total # of selection=2C1*8C2*6C2*4C1=3360

Answer: D.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618619 [10]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   25 Oct 2009, 19:38
7
Kudos
3
Bookmarks
Expert Reply
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.
General Discussion
User avatar
bmwhype2
VP
VP
Joined: 21 Jan 2007
Posts: 1346
Own Kudos [?]: 5010 [5]
Given Kudos: 4
Location: New York City
Send PM
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   25 Dec 2007, 17:48
4
Kudos
1
Bookmarks
I hope this is NOT a GMATprep question....


There are 4 slots.

_ _ _ _

2C1 * 8C2 * 6C2 * 4C1
= 2 * 28 * 15 * 4
= 56 * 60
= 3360

Recognize that for the second slot, we only have 10-2 = 8 elements to choose from. We need 2 of 8 elements to fill that spot. 8C2
For the third slot, we only have 6 elements left to choose from. We need to fill it with 2 elements.
User avatar
B
walker
SVP
SVP
Joined: 17 Nov 2007
Posts: 2408
Own Kudos [?]: 10035 [0]
Given Kudos: 361
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Send PM
GMAT ToolKit User
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   25 Dec 2007, 19:18
Expert Reply
jimjohn wrote:
Coach Miller is filling out the starting lineup for his indoor soccer team. There are 10 boys on th team, and he must assign 6 starters to the following positions: 1 goalkeeper, 2 on defense, 2 in midfield, and 1 forward. Only 2 of the boys can play goalkeeper, and they cannot play any other positions. The other boys can each play any of the other positions. How many different groupings are possible?

A) 60

B) 210

C) 2580

D) 3360

E) 151200


N=8P5*2P1/(2P2*2P2)=3360
User avatar
sondenso
Director
Director
Joined: 04 May 2006
Posts: 866
Own Kudos [?]: 6809 [0]
Given Kudos: 1
Concentration: Finance
Schools:CBS, Kellogg
Send PM
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   05 Jan 2008, 21:04
walker wrote:
N=8P5*2P1/(2P2*2P2)=3360


Walker,

I cant get it. Why it is not C, but P here or your resulting calculation is random, pl give yr logic explaination!
User avatar
B
walker
SVP
SVP
Joined: 17 Nov 2007
Posts: 2408
Own Kudos [?]: 10035 [4]
Given Kudos: 361
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Send PM
GMAT ToolKit User
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   06 Jan 2008, 00:27
3
Kudos
1
Bookmarks
Expert Reply
sondenso wrote:
I cant get it. Why it is not C, but P here or your resulting calculation is random, pl give yr logic explaination!


N=8P5*2P1/(2P2*2P2)=3360
8P5 - we choose 5 boys of 8 (without goalkeepers) for 5 positions: 2 on defense, 2 in midfield, and 1 forward.
2P2*2P2 - we can change position within 2 on defense, 2 in midfield. So, we should exclude this variations.
2P1=2C1 - we choose goalkeeper of 2 boys
User avatar
rvthryet
Intern
Intern
Joined: 02 Oct 2009
Posts: 15
Own Kudos [?]: 203 [2]
Given Kudos: 5
Send PM
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   25 Oct 2009, 18:57
2
Kudos
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:
User avatar
deepakraam
Manager
Manager
Joined: 15 Sep 2009
Posts: 55
Own Kudos [?]: 47 [2]
Given Kudos: 2
Send PM
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   26 Oct 2009, 07:12
2
Kudos
2 goal keepers can be selected in 2 ways.

Rest 5 positions has to be filled from 8 boys.

2 Defence can be selected in 8C2 ways

2 Midfielder can be selected in 6C2 ways

1 forward can be selected in 4C1 ways.

So the total combinations 8*28*15*4 = 3360 ways
avatar
subhajeet
Manager
Manager
Joined: 12 Jun 2010
Status:MBA Aspirant
Posts: 79
Own Kudos [?]: 247 [0]
Given Kudos: 1
Location: India
Concentration: Finance, International Business
WE:Information Technology (Investment Banking)
Send PM
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   02 Feb 2012, 21:30
Bunuel wrote:
rvthryet wrote:
A Coach is filling out the starting lineup for his indoor soccer team. There are 10 boys on the team, and he must assign 6 starters to the following positions: 1 goalkeeper, 2 on defence, 2 in midfield, and 1 forward. Only 2 of the boys can play goalkeeper, and they cannot play any other positions. The other boys can each play any of the other positions. How many different groupings are possible?

A) 60

B) 210

C) 2580

D) 3360

E) 151200


2C1 select 1 goalkeeper from 2 boys;
8C2 select 2 defense from 8 boys (as 2 boys can only play goalkeeper 10-2=8);
6C2 select 2 midfield from 6 boys (as 2 boys can only play goalkeeper and 2 we've already selected for defense 10-2-2=6);
4C1 select 1 forward from 4 boys (again as 2 boys can play only goalkeeper, 4 we've already selected for defense and midfield 10-2-4=4)

Total # of selection=2C1*8C2*6C2*4C1=3360

Answer: D.

Bunnel for these type of question do we need to follow the positions as given in the question stem. Cant we first select 1 forward first and then the defence and midfield. If we go this way the no of selections will become 2c1*8c1*7c2*5c2. Lemme know your views on this
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618619 [1]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   02 Feb 2012, 23:47
1
Kudos
Expert Reply
subhajeet wrote:
Bunnel for these type of question do we need to follow the positions as given in the question stem. Cant we first select 1 forward first and then the defence and midfield. If we go this way the no of selections will become 2c1*8c1*7c2*5c2. Lemme know your views on this


You can choose 2 in defense, 2 in midfield, and 1 forward from 8 in ANY order, you'l get the same result. The formula gives # of different selections of 2, 2, and 1 possible from 8, so the result must be the same despite the order in which you make this selections.
User avatar
sdas
Senior Manager
Senior Manager
Joined: 23 Mar 2011
Posts: 365
Own Kudos [?]: 637 [0]
Given Kudos: 59
Location: India
Schools: Rotman '16 Ivey '15 Queens'16 INSEAD Jan '16
GPA: 2.5
WE:Operations (Hospitality and Tourism)
Send PM
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   05 Feb 2012, 12:08
Hi Bunuel, I am not clear as to do this with P or C...though your answer with C matches mine with P. My explanation is same as Walkers. except for goalkeepers all other positions are common - should we not then divide by 2P2*2P2? Since selecting 2 goalkeepers was critical in terms of order - i used P.pls advice
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618619 [0]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   05 Feb 2012, 12:31
Expert Reply
sdas wrote:
Hi Bunuel, I am not clear as to do this with P or C...though your answer with C matches mine with P. My explanation is same as Walkers. except for goalkeepers all other positions are common - should we not then divide by 2P2*2P2? Since selecting 2 goalkeepers was critical in terms of order - i used P.pls advice


P and C just represent different formulas, different ways of counting. Most combinations questions can be solved in multiple ways, and if you understand the concept it really doesn't matter which approach you take.

As for this question: since we are dealing with different groups to be chosen from total and the order in each specific group doesn't matter I would use the method described in my previous post. It seems more straightforward and easy, at least for me.
User avatar
Nadezda
Intern
Intern
Joined: 12 Oct 2012
Posts: 9
Own Kudos [?]: 11 [3]
Given Kudos: 4
Location: Singapore
Concentration: International Business, General Management
Schools: INSEAD Jan '13 (M)
GMAT 1: 710 Q49 V35
GPA: 3.65
Send PM
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   05 Nov 2012, 21:07
2
Kudos
1
Bookmarks
The formula can be simplified for slot method.

First is goalkeeper restriction: 2 options.
Next: Out of rest 8 players we need to fill slots with 2, 2, 1 and 3 (non-assigned) players.
Numbers of people in the same position are listed in denumeretor with factorial.

8! / (2! x 2! x 1! x 3!) = 1680
2 x 1680 = 3360.

As you can see the order of picking players doesnt matter.

Solution of Bunuel simply leads to the same formula:
\(2 * \frac{8!}{2!6!} * \frac{6!}{2!4!} * \frac{4!}{1!3!} = 2 * \frac{8!}{2!2!3!}\)
User avatar
mbaiseasy
Senior Manager
Senior Manager
Joined: 13 Aug 2012
Posts: 336
Own Kudos [?]: 1821 [2]
Given Kudos: 11
Concentration: Marketing, Finance
Schools: Full Time MBA (A$)
GPA: 3.23
Send PM
GMAT ToolKit User
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   28 Dec 2012, 04:45
2
Kudos
rvthryet wrote:
A Coach is filling out the starting lineup for his indoor soccer team. There are 10 boys on the team, and he must assign 6 starters to the following positions: 1 goalkeeper, 2 on defence, 2 in midfield, and 1 forward. Only 2 of the boys can play goalkeeper, and they cannot play any other positions. The other boys can each play any of the other positions. How many different groupings are possible?

A. 60
B. 210
C. 2580
D. 3360
E. 151200


How many ways to select goal keeper? 2 only, others cannot do it
How many ways to select 2 in midfield? \(=\frac{8!}{2!6!}=28\)
How many ways to select 2 on defence? \(=\frac{6!}{2!4!}=15\)
How many ways to select 1 in forward? \(=\frac{4!}{3!1!}=4\)

\(2*28*15*4 = 120*28 = 3360\)

Answer: D
User avatar
nkimidi7y
Intern
Intern
Joined: 09 Apr 2012
Posts: 48
Own Kudos [?]: 191 [6]
Given Kudos: 29
Send PM
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   09 Feb 2013, 10:59
5
Kudos
1
Bookmarks
I always preferred slot method to solve these problems since childhood.

But my following approach gave me a wrong answer.
2 8 7 6 5 4 =13440.

What i forgot to do is divide (8*7) with 2 and 6*5 with another 2(since order doesnt matter between 2 defenders and 2 midfielders).

One of the other way of doing this is.

\(2P1\)\(*8P5\)/2*2.
avatar
Rohan_Kanungo
Intern
Intern
Joined: 10 Dec 2013
Posts: 14
Own Kudos [?]: 10 [0]
Given Kudos: 7
Location: India
Concentration: Technology, Strategy
Schools: ISB '16 (S)
GMAT 1: 710 Q48 V38
GPA: 3.9
WE:Consulting (Consulting)
Send PM
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   28 Jan 2014, 11:40
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?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618619 [0]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   29 Jan 2014, 08:45
Expert Reply
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.
User avatar
cumulonimbus
Manager
Manager
Joined: 14 Nov 2011
Posts: 100
Own Kudos [?]: 56 [0]
Given Kudos: 103
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE:Consulting (Manufacturing)
Send PM
GMAT ToolKit User
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   09 Jun 2014, 07:48
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
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618619 [0]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink] New post   09 Jun 2014, 09:20
Expert Reply
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
GMAT Club Bot
gmatclubot
Re: Coach Miller is filling out the starting lineup for his indoor soccer [#permalink]
09 Jun 2014, 09:20
 1   2   
Moderators:
Bunuel
Math Expert
92883 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions