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# Six highschool boys gather at the gym for a modified game

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Manager
Joined: 20 Jun 2012
Posts: 95
Location: United States
Concentration: Finance, Operations
GMAT 1: 710 Q51 V25
Six highschool boys gather at the gym for a modified game [#permalink]

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20 Oct 2013, 13:45
2
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Difficulty:

65% (hard)

Question Stats:

49% (00:49) correct 51% (01:27) wrong based on 188 sessions

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Six highschool boys gather at the gym for a modified game of basketball involving three teams. Three teams of 2 people each will be created. How many ways are there to create these 3 teams?

(A) 15
(B) 30
(C) 42
(D) 90
(E) 108
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 44399
Re: Six highschool boys gather at the gym for a modified game [#permalink]

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20 Oct 2013, 14:31
Expert's post
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stunn3r wrote:
Six highschool boys gather at the gym for a modified game of basketball involving three teams. Three teams of 2 people each will be created. How many ways are there to create these 3 teams?

(A) 15
(B) 30
(C) 42
(D) 90
(E) 108

$$\frac{C^2_6*C^2_4*C^2_2}{3!}=15$$ (dividing by 3! because the order of the teams doesn't matter).

For more on this check:
a-group-of-8-friends-want-to-play-doubles-tennis-how-many-55369.html
in-how-many-different-ways-can-a-group-of-9-people-be-85993.html
probability-88685.html
probability-85993.html
combination-55369.html
sub-committee-86346.html

Hope it helps.
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Manager
Joined: 26 Sep 2013
Posts: 210
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Re: Six highschool boys gather at the gym for a modified game [#permalink]

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20 Oct 2013, 20:31
Bunuel wrote:
stunn3r wrote:
Six highschool boys gather at the gym for a modified game of basketball involving three teams. Three teams of 2 people each will be created. How many ways are there to create these 3 teams?

(A) 15
(B) 30
(C) 42
(D) 90
(E) 108

$$\frac{C^2_6*C^2_4*C^2_2}{3!}=15$$ (dividing by 3! because the order of the teams doesn't matter).

For more on this check:
a-group-of-8-friends-want-to-play-doubles-tennis-how-many-55369.html
in-how-many-different-ways-can-a-group-of-9-people-be-85993.html
probability-88685.html
probability-85993.html
combination-55369.html
sub-committee-86346.html

Hope it helps.

Why does team order not mattering result in the 3! ending up in the divisor?
Intern
Joined: 07 Jan 2013
Posts: 40
Location: India
Concentration: Finance, Strategy
GMAT 1: 570 Q46 V23
GMAT 2: 710 Q49 V38
GPA: 2.9
WE: Information Technology (Computer Software)
Re: Six highschool boys gather at the gym for a modified game [#permalink]

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21 Oct 2013, 11:43
AccipiterQ wrote:
Bunuel wrote:
stunn3r wrote:
Six highschool boys gather at the gym for a modified game of basketball involving three teams. Three teams of 2 people each will be created. How many ways are there to create these 3 teams?

(A) 15
(B) 30
(C) 42
(D) 90
(E) 108

$$\frac{C^2_6*C^2_4*C^2_2}{3!}=15$$ (dividing by 3! because the order of the teams doesn't matter).

For more on this check:
a-group-of-8-friends-want-to-play-doubles-tennis-how-many-55369.html
in-how-many-different-ways-can-a-group-of-9-people-be-85993.html
probability-88685.html
probability-85993.html
combination-55369.html
sub-committee-86346.html

Hope it helps.

Why does team order not mattering result in the 3! ending up in the divisor?

Hi,

It is because we are just asked to select 3 teams and not concerned with relative order. Say we have selected 3 teams ABC , now the other orders BCA or CAB are the same teams. total there are 6 outcomes if we consider the orders

I think for this purpose we can just have 6C2 teams , meaning we are just finding 2 items out of six to form a team which yield 15
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Manager
Joined: 05 Jun 2013
Posts: 53
Location: India
Concentration: Entrepreneurship, General Management
GMAT 1: 640 Q48 V29
GPA: 3.6
WE: Business Development (Education)
Re: Six highschool boys gather at the gym for a modified game [#permalink]

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21 Oct 2013, 12:06
stunn3r wrote:
Six highschool boys gather at the gym for a modified game of basketball involving three teams. Three teams of 2 people each will be created. How many ways are there to create these 3 teams?

(A) 15
(B) 30
(C) 42
(D) 90
(E) 108

To put it in a different way:
Say 6 boys are a,b,c,d,e,f and we need to form 3 teams say t1,t2,t3

With a : a,b a,c a,d a,e a,f --->5
With b : b,c b,d b,e b,f --->4
With c : c,d c,e c,f --->3
With d : d,e d,f --->2
With e : e,f --->1
With f : --- --->0

Hence Total is 5+4+3+2+1+0 = 15.

Hence 15 such teams are possible

-- Omkar

In with with 'kudos' -- gmatclub
Senior Manager
Joined: 08 Apr 2012
Posts: 437
Re: Six highschool boys gather at the gym for a modified game [#permalink]

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22 Oct 2013, 09:27
Bunuel wrote:
stunn3r wrote:
Six highschool boys gather at the gym for a modified game of basketball involving three teams. Three teams of 2 people each will be created. How many ways are there to create these 3 teams?

(A) 15
(B) 30
(C) 42
(D) 90
(E) 108

$$\frac{C^2_6*C^2_4*C^2_2}{3!}=15$$ (dividing by 3! because the order of the teams doesn't matter).

For more on this check:
a-group-of-8-friends-want-to-play-doubles-tennis-how-many-55369.html
in-how-many-different-ways-can-a-group-of-9-people-be-85993.html
probability-88685.html
probability-85993.html
combination-55369.html
sub-committee-86346.html

Hope it helps.

I do not understand why there is no division for each team by 2?
For a given team, it does not matter if player a was select first and then player b, or visa versa.
Pls. help
Manager
Joined: 05 Jun 2013
Posts: 53
Location: India
Concentration: Entrepreneurship, General Management
GMAT 1: 640 Q48 V29
GPA: 3.6
WE: Business Development (Education)
Re: Six highschool boys gather at the gym for a modified game [#permalink]

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22 Oct 2013, 09:35
ronr34 wrote:
Bunuel wrote:
stunn3r wrote:
Six highschool boys gather at the gym for a modified game of basketball involving three teams. Three teams of 2 people each will be created. How many ways are there to create these 3 teams?

(A) 15
(B) 30
(C) 42
(D) 90
(E) 108

$$\frac{C^2_6*C^2_4*C^2_2}{3!}=15$$ (dividing by 3! because the order of the teams doesn't matter).

For more on this check:
a-group-of-8-friends-want-to-play-doubles-tennis-how-many-55369.html
in-how-many-different-ways-can-a-group-of-9-people-be-85993.html
probability-88685.html
probability-85993.html
combination-55369.html
sub-committee-86346.html

Hope it helps.

I do not understand why there is no division for each team by 2?
For a given team, it does not matter if player a was select first and then player b, or visa versa.
Pls. help

Hi Ron,

Your question is not clear. Can you please elaborate.
Manager
Joined: 24 Apr 2013
Posts: 66
Location: United States
Re: Six highschool boys gather at the gym for a modified game [#permalink]

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22 Oct 2013, 09:36
Bunuel wrote:
stunn3r wrote:
Six highschool boys gather at the gym for a modified game of basketball involving three teams. Three teams of 2 people each will be created. How many ways are there to create these 3 teams?

(A) 15
(B) 30
(C) 42
(D) 90
(E) 108

$$\frac{C^2_6*C^2_4*C^2_2}{3!}=15$$ (dividing by 3! because the order of the teams doesn't matter).

Hope it helps.

Bunuel,

I solved it differently: $$C^2_6$$ to get the number of ways for one team to be created multiplied by 3 for three teams. = $$C^2_6$$ * 3 =15
Is this logic flawed?
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Posts: 437
Re: Six highschool boys gather at the gym for a modified game [#permalink]

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22 Oct 2013, 09:46
kulkarnios wrote:
ronr34 wrote:
I do not understand why there is no division for each team by 2?
For a given team, it does not matter if player a was select first and then player b, or visa versa.
Pls. help

Hi Ron,

Your question is not clear. Can you please elaborate.

The numerator is all the options to take all the teams (choose two from 6, then choose 2 from 4)
The we divide this by 3! so that we take into account all possible permutations of the teams.
But for each team, of player a and player b, it is the same team if a is chosen first and then b, just as if
b were chosen first and then a.
So to my logic, we need to divide each team for example 6C2 by 2 to take that into account....
no?
Math Expert
Joined: 02 Sep 2009
Posts: 44399
Re: Six highschool boys gather at the gym for a modified game [#permalink]

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22 Oct 2013, 09:48
The links in my post might help.
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Posts: 8001
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Re: Six highschool boys gather at the gym for a modified game [#permalink]

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30 Sep 2014, 02:32
1
KUDOS
Expert's post
Quote:
where am i going wrong in this :

lets say we have 1,2,3,4,5,6 boys

we need to make 3 teams of two members each

lets says for the 1st team i chose any two boys ( so it is 6c2 i.e 15 ways )
now two members are out and i am left with 4 boys ,,,now i agn chose 2 boys out of 4 ( 4c2....6 ways )

now only two members will be left and they will form the third team

so total no of ways 15 * 6 = 90

You have selected the "first team", the "second team" and the "third team" i.e. you have ordered the teams. Say, you select A and B for first team, C and D for second team and E and F for the third team. Now say you select C and D for first team, A and B for second team and E and F for third team. Are they different selections? No. We just need 3 teams. The three teams are A and B, C and D and E and F in both cases. So we need to divide the teams we obtain by 3! to get rid of the team arrangement.

90/3! = 15 (correct answer)
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Posts: 35
Re: Six highschool boys gather at the gym for a modified game [#permalink]

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30 Sep 2014, 06:36
VeritasPrepKarishma wrote:
Quote:
where am i going wrong in this :

lets say we have 1,2,3,4,5,6 boys

we need to make 3 teams of two members each

lets says for the 1st team i chose any two boys ( so it is 6c2 i.e 15 ways )
now two members are out and i am left with 4 boys ,,,now i agn chose 2 boys out of 4 ( 4c2....6 ways )

now only two members will be left and they will form the third team

so total no of ways 15 * 6 = 90

You have selected the "first team", the "second team" and the "third team" i.e. you have ordered the teams. Say, you select A and B for first team, C and D for second team and E and F for the third team. Now say you select C and D for first team, A and B for second team and E and F for third team. Are they different selections? No. We just need 3 teams. The three teams are A and B, C and D and E and F in both cases. So we need to divide the teams we obtain by 3! to get rid of the team arrangement.

90/3! = 15 (correct answer)

it is always there if we look....thanks for the explanation and taking the time out ....
+1
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Six highschool boys gather at the gym for a modified game [#permalink]

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30 Aug 2017, 09:05
LET ME HAVE PLEASURE TO INTRODUCE A SMALL METHOD

6 PERSONS
3 TEAMS
2 PERSON IN EACH TEAM

NO OF WAYS = 6!/(3!2!2!2!)
that is = 2! will come the n number of times here as n=3 so they are coming 3 times 2!2!2!

6!/3!2!2!2! = 15

Ans is A

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# Six highschool boys gather at the gym for a modified game

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