A Coach is filling out the starting lineup for his indoor : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 14:59

### 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

# A Coach is filling out the starting lineup for his indoor

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

### Hide Tags

Intern
Joined: 02 Oct 2009
Posts: 16
Followers: 0

Kudos [?]: 40 [3] , given: 5

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

### Show Tags

25 Oct 2009, 16:43
3
KUDOS
10
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

66% (03:06) correct 34% (02:21) wrong based on 278 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Jul 2012, 00:39, edited 2 times in total.
Edited the question and added the OA
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93661 [4] , given: 10583

Re: Combination or Permutation: Can't make up my mind :) [#permalink]

### Show Tags

25 Oct 2009, 18:38
4
KUDOS
Expert's post
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

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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93661 [3] , given: 10583

Re: Combination or Permutation: Can't make up my mind :) [#permalink]

### Show Tags

25 Oct 2009, 17:08
3
KUDOS
Expert's post
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

_________________
Intern
Joined: 12 Oct 2012
Posts: 11
Location: Singapore
Concentration: International Business, General Management
GMAT 1: 710 Q49 V35
GPA: 3.65
Followers: 1

Kudos [?]: 11 [2] , given: 4

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

### Show Tags

05 Nov 2012, 20:07
2
KUDOS
1
This post was
BOOKMARKED
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:
$$2 * \frac{8!}{2!6!} * \frac{6!}{2!4!} * \frac{4!}{1!3!} = 2 * \frac{8!}{2!2!3!}$$
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1183
Followers: 422

Kudos [?]: 1512 [2] , given: 4

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

### Show Tags

23 Sep 2014, 09:38
2
KUDOS
Expert's post
usre123 wrote:

the problem is, that when selecting president and VP from a group, order shouldn't be important. AB or BA is the same

If you're choosing a President and Vice-President, and you choose A for President and B for VP, that's very different from choosing B for President and A for VP -- you have a different President! So when you're choosing a President and VP, order is very important, and AB and BA are not the same selection.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Intern
Joined: 02 Oct 2009
Posts: 16
Followers: 0

Kudos [?]: 40 [1] , given: 5

Re: Combination or Permutation: Can't make up my mind :) [#permalink]

### Show Tags

25 Oct 2009, 17:57
1
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
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 434 [1] , given: 11

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

### Show Tags

28 Dec 2012, 03:45
1
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? $$=\frac{4!}{3!1!}=4$$

$$2*28*15*4 = 120*28 = 3360$$

_________________

Impossible is nothing to God.

Manager
Joined: 13 Oct 2012
Posts: 78
Concentration: General Management, Leadership
Schools: IE '15 (A)
GMAT 1: 760 Q49 V46
Followers: 1

Kudos [?]: -12 [1] , given: 0

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

### Show Tags

03 Jan 2013, 22:56
1
KUDOS
2C1 * 8C2 * 6C2 * 4C1
Ans - D
Manager
Joined: 09 Apr 2012
Posts: 62
Followers: 0

Kudos [?]: 53 [1] , given: 27

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

### Show Tags

09 Feb 2013, 09:59
1
KUDOS
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.
Intern
Status: At the end all are winners, Some just take a little more time to win.
Joined: 08 Oct 2013
Posts: 23
Location: India
Concentration: Finance, Accounting
GMAT Date: 11-20-2013
GPA: 3.97
WE: Consulting (Computer Software)
Followers: 0

Kudos [?]: 8 [1] , given: 45

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

### Show Tags

25 Oct 2013, 02:20
1
KUDOS
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.
Senior Manager
Affiliations: PMP
Joined: 13 Oct 2009
Posts: 312
Followers: 4

Kudos [?]: 161 [0], given: 37

Re: Combination or Permutation: Can't make up my mind :) [#permalink]

### Show Tags

25 Oct 2009, 18:55
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

For that matter we could have gone an extra step and said it should be 9c6 (leaving other goalie out) , but for Bunuel explanation )
Bunuel is awesome.. of course this time I was clear too and I in fact prepared a similar example as Bunuel
_________________

Thanks, Sri
-------------------------------
keep uppp...ing the tempo...

Press +1 Kudos, if you think my post gave u a tiny tip

Manager
Joined: 15 Sep 2009
Posts: 137
Followers: 1

Kudos [?]: 22 [0], given: 2

Re: Combination or Permutation: Can't make up my mind :) [#permalink]

### Show Tags

26 Oct 2009, 06:12
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
Senior Manager
Joined: 08 Nov 2010
Posts: 417
WE 1: Business Development
Followers: 7

Kudos [?]: 106 [0], given: 161

Re: Combination or Permutation: Can't make up my mind :) [#permalink]

### Show Tags

05 Feb 2011, 06:40
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.
_________________
Intern
Joined: 13 Jun 2010
Posts: 18
Followers: 0

Kudos [?]: 15 [0], given: 0

Re: Combination or Permutation: Can't make up my mind :) [#permalink]

### Show Tags

12 Nov 2011, 02:17
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

Sorry for bringing up an old post. I am clear with the above explanation except for one fact . Is there a necessity to choose in the above order. What happens if I choose the goalie, then the forward and then the defense & midfield. In such a case the combinations change drastically.

2C1 * 8C1 * 6C2 *4C2 = 1440.

The questions does not specify any order with selecting one group over another.
Can someone please explain this?
Intern
Joined: 09 Nov 2004
Posts: 13
Followers: 0

Kudos [?]: 5 [0], given: 1

Re: Combination or Permutation: Can't make up my mind :) [#permalink]

### Show Tags

12 Nov 2011, 15:32
gmatrant wrote:
Sorry for bringing up an old post. I am clear with the above explanation except for one fact . Is there a necessity to choose in the above order. What happens if I choose the goalie, then the forward and then the defense & midfield. In such a case the combinations change drastically.

2C1 * 8C1 * 6C2 *4C2 = 1440.

The questions does not specify any order with selecting one group over another.
Can someone please explain this?

That would still work. Except that there is a mistake in the counting you did
2C1 * 8C1 * 7C2* 5C2 = 3360
Senior Manager
Joined: 12 Oct 2011
Posts: 272
Followers: 0

Kudos [?]: 47 [0], given: 110

Re: Combination or Permutation: Can't make up my mind :) [#permalink]

### Show Tags

04 Jan 2012, 22:00
Nice question. Easy to make the 8C5 trap. The individual selections need to be made and that, IMO, is the key to this problem. Answer is D.
_________________

Consider KUDOS if you feel the effort's worth it

Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 178
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)
Followers: 3

Kudos [?]: 80 [0], given: 1

Re: Combination or Permutation: Can't make up my mind :) [#permalink]

### Show Tags

02 Feb 2012, 20:30
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

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
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93661 [0], given: 10583

Re: Combination or Permutation: Can't make up my mind :) [#permalink]

### Show Tags

02 Feb 2012, 22:47
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.
_________________
Manager
Joined: 10 Jan 2011
Posts: 244
Location: India
GMAT Date: 07-16-2012
GPA: 3.4
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 57 [0], given: 25

Re: Combination or Permutation: Can't make up my mind :) [#permalink]

### Show Tags

03 Jul 2012, 20:41
abhi47 wrote:
Guys,

Is it possible to solve this problem using the slot method ? Please clarify.

Yes it is possible to solve this problem using slot method: here is how I solved it

There are five slot's and ten players.

Most restricted slot is goal keeper: 2 players can go for that slot

Next is defender : out of 8 two can be selected : 8c2 = 28

Next is midfielder : out of remaining 6 two can be selected: 6c2 = 15

Next is forward : out of 4 1 can be selected : 4c1 = 4

Hence, total number of ways for selecting players = 2*28*15*4 = 3360

hope it is clear
_________________

-------Analyze why option A in SC wrong-------

Intern
Joined: 21 Oct 2012
Posts: 26
GMAT Date: 01-19-2013
Followers: 1

Kudos [?]: 7 [0], given: 15

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

### Show Tags

17 Nov 2012, 10:52
I did it in the next way:
1) ways to chose Goalkeepers - it's obvious 1C2=2
2) ways to chose Field players within the group - comes from DDMMF p=5!/2!2!=30
3) ways to chose Field players from 8 possible options - 5C8=56

Multiple everything: 2*30*56=3360

However the previous comment is the most elegant
_________________

MGMAT1 - 610
MGMAT2 - 670
MGMAT3 - 640

OMG

Re: A Coach is filling out the starting lineup for his indoor   [#permalink] 17 Nov 2012, 10:52

Go to page    1   2    Next  [ 32 posts ]

Similar topics Replies Last post
Similar
Topics:
In Sam's hanger there are 23 boxes, 16 out of the boxes are filled 2 19 Jun 2016, 09:58
12 A certain football coach allows his quarterback to call thre 6 12 Jul 2014, 22:52
3 Jim filled his dog's bowl with 80 dog food pellets. Starting 3 25 May 2014, 14:01
11 A pump started filling an empty pool with water and continue 8 20 Nov 2008, 10:30
15 Coach Miller is filling out the starting lineup for his 18 25 Dec 2007, 15:44
Display posts from previous: Sort by

# A Coach is filling out the starting lineup for his indoor

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.