It is currently 20 Oct 2017, 16:31

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Coach Miller is filling out the starting lineup for his

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 19 Aug 2007
Posts: 167

Kudos [?]: 66 [1], given: 0

Coach Miller is filling out the starting lineup for his [#permalink]

### Show Tags

25 Dec 2007, 16:44
1
KUDOS
8
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

65% (02:20) correct 35% (02:32) wrong based on 560 sessions

### HideShow 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-coach-is-filling-out-the-starting-lineup-for-his-indoor-85800.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Jun 2013, 02:37, edited 2 times in total.

Kudos [?]: 66 [1], given: 0

CEO
Joined: 21 Jan 2007
Posts: 2734

Kudos [?]: 1049 [4], given: 4

Location: New York City

### Show Tags

25 Dec 2007, 17:48
4
KUDOS
1
This post was
BOOKMARKED
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.

Kudos [?]: 1049 [4], given: 4

CEO
Joined: 21 Jan 2007
Posts: 2734

Kudos [?]: 1049 [0], given: 4

Location: New York City

### Show Tags

25 Dec 2007, 18:32
jimjohn wrote:
thanks. that was from princeton
but how do you know to break it up into:
(8 C 2) * (6 C 2) * (4 C 1)

instead of just doing (8 C 5)

8c5 means there is one slot where we choose 5 from 8 elements.

Kudos [?]: 1049 [0], given: 4

Director
Joined: 03 Sep 2006
Posts: 865

Kudos [?]: 1071 [0], given: 33

Re: PS permutations/combinations [#permalink]

### Show Tags

25 Dec 2007, 19:18
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

2C1 * 8C2*6C2*4C1

This is important to note, we have already chosen 2 goalkeeprs, so we are left with 8 people, and then after choosing 2 defense, we are left with 6 out of which to choose 2 midfield and then we are left with 4.

Hmm...but a good question... and it can be missed during the real exam! If proper attention is not paid!

Kudos [?]: 1071 [0], given: 33

SVP
Joined: 04 May 2006
Posts: 1881

Kudos [?]: 1399 [0], given: 1

Schools: CBS, Kellogg

### Show Tags

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!
_________________

Kudos [?]: 1399 [0], given: 1

CEO
Joined: 17 Nov 2007
Posts: 3584

Kudos [?]: 4586 [2], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

### Show Tags

06 Jan 2008, 00:27
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
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
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Kudos [?]: 4586 [2], given: 360

Director
Joined: 09 Jul 2005
Posts: 589

Kudos [?]: 64 [1], given: 0

### Show Tags

07 Jan 2008, 05:14
1
KUDOS
vscid wrote:
jimjohn wrote:
thanks. that was from princeton
but how do you know to break it up into:
(8 C 2) * (6 C 2) * (4 C 1)

instead of just doing (8 C 5)

bmwhype2
I still have not understood why it can't be 8c5.
Can you explain in detail?

If you consider 8C5, you are missing all the possible positions of the players. In a group of 5 players the coach can built many teams just switching the positions of those 5 players.

This problem has many approachs:

1st approach: n=2*C(8,5)*C(5,2)*C(3,2) = 3360; where you first consider two players for the goalkeeper position [2], second all the possible groups of 5 players from 8 players [C(8,5)] and third and last all the possible positions of all those 5 players [C(5,2)*C(3,2)].

2nd approach: n=2*8!/3!= 13440, number to which you have to discount all the permutations among defenses and midfields, i.e. 2! and 2!. Therefore 13440/[2!·2!]=3360

3th approach: n=2*C(8,2)*C(6,2)*C(4,1)=3360; you just has to consider how many players you can fill the positions with. Since there is no difference between mildfield1 and mildfield2 you "count" combinations. If not, you should count permutations.

Kudos [?]: 64 [1], given: 0

Senior Manager
Joined: 31 Jul 2008
Posts: 290

Kudos [?]: 55 [0], given: 0

Re: PS permutations/combinations [#permalink]

### Show Tags

25 Aug 2008, 13:27
i have small doubt ;

in the approach 2C18C26C24C1

why are selecting from 8 players whereas we will be left with 9 players after we made a selection for the goal keeper (as that is the logic stated in the solution for 6C2 i.e we are choosing from 6 because we will be left with 6 after selecting 2 from 8)

Kudos [?]: 55 [0], given: 0

Senior Manager
Joined: 07 Jan 2008
Posts: 398

Kudos [?]: 292 [0], given: 0

Re: PS permutations/combinations [#permalink]

### Show Tags

13 Mar 2009, 13:13
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

2C1*8C5*5C2*3C2 = 3360
or
2C1*8C5*5C1*4C2 = 3360

Kudos [?]: 292 [0], given: 0

Manager
Joined: 27 Oct 2008
Posts: 185

Kudos [?]: 164 [1], given: 3

Re: PS permutations/combinations [#permalink]

### Show Tags

27 Sep 2009, 11:53
1
KUDOS
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

Soln:
1 goal keeper can be chosen from 2 boys in 2C1 ways.
2 defenders can be chosen from 8 boys in 8C2 ways
2 midfielders can be chosen from left over 6 boys in 6C2 ways
1 forwards can be chosen from the left over 4 boys in 4C1 ways

Thus total number of ways of choosing team is
= 2C1 * 8C2 * 6C2 * 4C1
= 3360

Ans is D

Kudos [?]: 164 [1], given: 3

Senior Manager
Joined: 22 Dec 2009
Posts: 356

Kudos [?]: 415 [0], given: 47

Re: PS permutations/combinations [#permalink]

### Show Tags

16 Feb 2010, 05:43
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

Goal Keeper selection = 2c1 Since only 2 can play at that position
Defence Selection = 8c2
Midfield Selection = 6c2
Forward Selection = 4c1

Total combinations = 2c1 x 8c2 x 6c2 x 4c1 = 2 x 24 x 15 x 4 = 3360
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~

Kudos [?]: 415 [0], given: 47

Senior Manager
Joined: 23 Mar 2011
Posts: 461

Kudos [?]: 279 [0], given: 59

Location: India
GPA: 2.5
WE: Operations (Hospitality and Tourism)
Re: Coach Miller is filling out the starting lineup for his [#permalink]

### Show Tags

05 Feb 2012, 00:50
I agree with walker - this is a permutation problem. As selecting 1 goalkeeper from 2 will result in 2 different teams. Likewise since each remaining players can play all positions - though order will matter, yet we need to divide by 2! for each positions to ensure there are no repetitions. Please correct me if I went wrong in my understanding.
_________________

"When the going gets tough, the tough gets going!"

Bring ON SOME KUDOS MATES+++

-----------------------------
Quant Notes consolidated: http://gmatclub.com/forum/consolodited-quant-guides-of-forum-most-helpful-in-preps-151067.html#p1217652

My GMAT journey begins: http://gmatclub.com/forum/my-gmat-journey-begins-122251.html

Kudos [?]: 279 [0], given: 59

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129034 [0], given: 12187

Re: Coach Miller is filling out the starting lineup for his [#permalink]

### Show Tags

05 Feb 2012, 01:27
sdas wrote:
I agree with walker - this is a permutation problem. As selecting 1 goalkeeper from 2 will result in 2 different teams. Likewise since each remaining players can play all positions - though order will matter, yet we need to divide by 2! for each positions to ensure there are no repetitions. Please correct me if I went wrong in my understanding.

I'm not sure I understand you point about the order. Anyway below is a different approach to this problem:

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

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

This problem is also discussed here: a-coach-is-filling-out-the-starting-lineup-for-his-indoor-85800.html

Hope it helps.
_________________

Kudos [?]: 129034 [0], given: 12187

Senior Manager
Joined: 23 Mar 2011
Posts: 461

Kudos [?]: 279 [0], given: 59

Location: India
GPA: 2.5
WE: Operations (Hospitality and Tourism)
Re: Coach Miller is filling out the starting lineup for his [#permalink]

### Show Tags

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
_________________

"When the going gets tough, the tough gets going!"

Bring ON SOME KUDOS MATES+++

-----------------------------
Quant Notes consolidated: http://gmatclub.com/forum/consolodited-quant-guides-of-forum-most-helpful-in-preps-151067.html#p1217652

My GMAT journey begins: http://gmatclub.com/forum/my-gmat-journey-begins-122251.html

Kudos [?]: 279 [0], given: 59

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129034 [0], given: 12187

Re: Coach Miller is filling out the starting lineup for his [#permalink]

### Show Tags

05 Feb 2012, 12:31
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.
_________________

Kudos [?]: 129034 [0], given: 12187

Manager
Joined: 22 Jan 2012
Posts: 88

Kudos [?]: 139 [0], given: 9

Location: India
Concentration: General Management, Technology
GPA: 3.3
WE: Engineering (Consulting)
Re: Coach Miller is filling out the starting lineup for his [#permalink]

### Show Tags

18 Mar 2012, 23:13

2C1 * 8C2 * 6C2 * 4C1

But what if order is not considered and the coach needs 3 defense players..
Does anyone have answer..

Hope this question stimulates something thinking..
_________________

Press +1 Kudos rather than saying thanks
which is more helpful infact..

Ill be posting good questions as many as I can...

Towards Success

Kudos [?]: 139 [0], given: 9

Manager
Joined: 22 Jan 2012
Posts: 88

Kudos [?]: 139 [0], given: 9

Location: India
Concentration: General Management, Technology
GPA: 3.3
WE: Engineering (Consulting)
Re: Coach Miller is filling out the starting lineup for his [#permalink]

### Show Tags

18 Mar 2012, 23:29
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, 3 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, without considering the order?
_________________

Press +1 Kudos rather than saying thanks
which is more helpful infact..

Ill be posting good questions as many as I can...

Towards Success

Kudos [?]: 139 [0], given: 9

Intern
Joined: 04 Jun 2013
Posts: 20

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

Location: India
Concentration: Strategy, Finance
GMAT 1: 680 Q49 V34
GPA: 3.7
WE: Research (Consulting)
Re: Coach Miller is filling out the starting lineup for his [#permalink]

### Show Tags

20 Jun 2013, 02:20
How many different groupings are possible? ...

This is a combination question based on the wording. The question asked for number of "Groups" and not the number of different plays.

Example, say the boys were b1, b2, b3, b4,...,b8 .. say you have group where b1 plays forward, b2 and b3 play mid, and b4, and b5 play back.. Now this is ONE group. This "group" does not change if only the player positions are changed.

Had the question been something like "Number of different plays", then I would go the permutation route which most people seem to agree with.

This is just my take, I maybe wrong in my assessment.

By my logic, the answer should be 112 [2 x 8C5] --> we need to select 1 goalkeeper from 2 people and 5 folks from the remaining 8, per me the question does not care which positions each person plays in.

Thanks.

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

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129034 [0], given: 12187

Re: Coach Miller is filling out the starting lineup for his [#permalink]

### Show Tags

20 Jun 2013, 02:36
ashgoel wrote:
How many different groupings are possible? ...

This is a combination question based on the wording. The question asked for number of "Groups" and not the number of different plays.

Example, say the boys were b1, b2, b3, b4,...,b8 .. say you have group where b1 plays forward, b2 and b3 play mid, and b4, and b5 play back.. Now this is ONE group. This "group" does not change if only the player positions are changed.

Had the question been something like "Number of different plays", then I would go the permutation route which most people seem to agree with.

This is just my take, I maybe wrong in my assessment.

By my logic, the answer should be 112 [2 x 8C5] --> we need to select 1 goalkeeper from 2 people and 5 folks from the remaining 8, per me the question does not care which positions each person plays in.

Thanks.

The correct answer is D. Your doubt is addressed here: a-coach-is-filling-out-the-starting-lineup-for-his-indoor-85800.html

Hope it helps.
_________________

Kudos [?]: 129034 [0], given: 12187

Re: Coach Miller is filling out the starting lineup for his   [#permalink] 20 Jun 2013, 02:36
Display posts from previous: Sort by

# Coach Miller is filling out the starting lineup for his

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.