Author 
Message 
TAGS:

Hide Tags

MBA Section Director
Joined: 19 Mar 2012
Posts: 5180
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]
Show Tags
18 May 2018, 00:11
Question Stats:
68% (01:16) correct 32% (01:53) wrong based on 92 sessions
HideShow timer Statistics





BSchool Forum Moderator
Joined: 05 Jul 2017
Posts: 398
Location: India
GPA: 4

Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]
Show Tags
18 May 2018, 00:32
souvik101990 wrote: Six marbles (two red, two blue, and two green) are arranged in two rows of three such that no single row or column has two marbles of the same color. How many different arrangements are possible? a. 12 b. 48 c. 96 d. 128 e. 192 Lets first fix the first row to be R  B  G and see the possibilities in the next 2 ROWS R  B  GB  G  R G  R  B And R  B  GG  R  B B  G  R So there are 2 cases, when we fix the first row. But the first row itself can be arranged in 3! i.e. 6 ways Now, from one of the example shown above, we know there are 2 possibilities/ fixed row Therefore, there will be 12 possibilities when there are 6 fixed rows Answer is A
_________________
My journey From 410 to 700 Here's my experience when I faced a glitch in my GMAT Exam Don't do this mistake when you give your GMATPrep Mock!



Manager
Joined: 30 May 2017
Posts: 116
Location: United States
GRE 1: 332 Q164 V168
GPA: 3.57

Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]
Show Tags
18 May 2018, 01:00
The maximum number of arrangement with 1 red, 1 blue and 1 green in first row is (3!) =6 The maximum number of arrangement with 1 red, 1 blue and 1 green in second row is (3!) =6 The maximum number of arrangement with only each color appearing once in each row is 6*6 =36. i.e. first row*second row = 36 With the restrictive conditions applied of the same color not on each columnLooking at the options we already know that only option A could be the answer, because it is the only option that is less than 36. Hence option A = 12 is the answer. There will be repetitions 2/3 of the time and no repetition 1/3 of the time. 1/3 of 36 = 12 All conditions possible are:BRGRGBBRGGBRRGBGBRRGBBRGGBRBRGGBRRGB
_________________
Kindly press the +1Kudos if you like the explanation. Thanks a lot!!!



Math Expert
Joined: 02 Aug 2009
Posts: 5898

Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]
Show Tags
18 May 2018, 01:12
souvik101990 wrote: Six marbles (two red, two blue, and two green) are arranged in two rows of three such that no single row or column has two marbles of the same color. How many different arrangements are possible? a. 12 b. 48 c. 96 d. 128 e. 192 let the position be A.....B....C D.....E....F now A can take any of three colours  3 colours B can take any of remaining 2  2 colours C can take the last one  1 colour D can take any of 2 except the one at A  2 colours E can take ONLY 1 since if D is the SAME as B, E has to be same as C otherwise C and F will be same colour. And if D is like C, E can be ONLY Asimilarly F will take 1 total 3*2*1*2*1*1=12 A
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
GMAT online Tutor



Manager
Joined: 07 Apr 2018
Posts: 106

Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]
Show Tags
18 May 2018, 01:19
Let's fix the first row of marble as R B G Possible ways to arrange the first row= 3! = 6 Second row can be B G R or G R B Second row can be arranged in 2 ways Therefore, total possibilities= 6 * 2 = 12 Correct Answer= A
_________________
Please +1 kudos if my post/reply helps !!



Manager
Joined: 05 Feb 2016
Posts: 113
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)

Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]
Show Tags
18 May 2018, 03:55
souvik101990 wrote: Six marbles (two red, two blue, and two green) are arranged in two rows of three such that no single row or column has two marbles of the same color. How many different arrangements are possible? a. 12 b. 48 c. 96 d. 128 e. 192 let the position be XYZ ABC X can take any of three colours  3 Y can take any of remaining 2  2 Z can take the last one  1 A can take any of 2 except the one at X  2 B can take ONLY 1 similarly C will take 1 total 3*2*1*2*1*1=12 A



Intern
Joined: 10 May 2016
Posts: 18
Location: India
GPA: 3.9

Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]
Show Tags
18 May 2018, 04:31
souvik101990 wrote: Six marbles (two red, two blue, and two green) are arranged in two rows of three such that no single row or column has two marbles of the same color. How many different arrangements are possible? a. 12 b. 48 c. 96 d. 128 e. 192 The correct answer is option A. Here is why:Since no row has two marbles of the same color it can a permutation of R, B and G. So, for the first row will be 3C1 ways i.e. 6. Now lets assume one possiblity as R, B, G. The subsequent row can only two possible combinations i.e. G , R, B or B, G, R So 6 ways to arrange the first row * 2 ways to arrange the second row = 12 Hence A.



Manager
Joined: 04 Apr 2015
Posts: 178

Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]
Show Tags
18 May 2018, 05:08
3 colors to be place in a row 3! ways no of rows 2 so 3!x2= 12
A



Intern
Joined: 26 Nov 2014
Posts: 7

Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]
Show Tags
20 May 2018, 04:06
souvik101990 wrote: Six marbles (two red, two blue, and two green) are arranged in two rows of three such that no single row or column has two marbles of the same color. How many different arrangements are possible? a. 12 b. 48 c. 96 d. 128 e. 192 There could be two approaches primarily 1) Using combinatorics there are 3 colors,two balls/color RED=2, Blue=2 and Green=2Now, there could be 2 options of choosing where to place the first ball i.e Row1 or Row2=2C1 There would be 3 options of choosing the first color i.e. R,B,G=3C1 if we have chosen the 1st color, 2nd and 3rd color has to be different i.e. let's say if we chose Red, We would have only B and green to be selected=2C1(1 out of 2) and 1C1 subsequently Hence total number of ways=2C1*3C1*2C1*1C1=12 2) There could be 3! possibilities of arranging a Red, a green and 1 Blue ball RBG,RGB,BGR,BRG,GRB and GBR. Now if we select any one of the 6 given combinations for row 1, we would only be able to select 1 out of 2 remaining combinations for Row 2( i.e for RGB in Row 1, we can select BRG and GBR only=> remaining combinations would have atleast one of the three colors in same position in column e.g. if we select GRB, Blue color will be same in 1st and 2nd row not allowed )= 6*2=12 or 2 options for RGB OR 2Option for RBG etc.....2+26 times=12 Please give kudos if it makes sense



Manager
Joined: 30 May 2017
Posts: 116
Location: United States
GRE 1: 332 Q164 V168
GPA: 3.57

Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]
Show Tags
28 May 2018, 06:35
souvik101990 wrote: Six marbles (two red, two blue, and two green) are arranged in two rows of three such that no single row or column has two marbles of the same color. How many different arrangements are possible? a. 12 b. 48 c. 96 d. 128 e. 192 souvik101990I am the winner of the question. How do I redeem the GMAT OnDemand Prep by Veritas Prep? Thank you very much.
_________________
Kindly press the +1Kudos if you like the explanation. Thanks a lot!!!



Manager
Joined: 30 May 2017
Posts: 116
Location: United States
GRE 1: 332 Q164 V168
GPA: 3.57

Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]
Show Tags
30 May 2018, 00:04
What is the reward for GST  GMAT Spring Training 2018? Is it just the GMAT Club Tests or does the reward include the GMAT OnDemand Prep by Veritas Prep?
_________________
Kindly press the +1Kudos if you like the explanation. Thanks a lot!!!



BSchool Forum Moderator
Joined: 05 Jul 2017
Posts: 398
Location: India
GPA: 4

Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]
Show Tags
30 May 2018, 10:16
Hey houston1980If you are the winner for this question, then will get the GMATClub subscription. If you are the overall winner for the entire week, then you will get the partner award. Hope this helps
_________________
My journey From 410 to 700 Here's my experience when I faced a glitch in my GMAT Exam Don't do this mistake when you give your GMATPrep Mock!



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570

Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]
Show Tags
31 May 2018, 16:13
souvik101990 wrote: Six marbles (two red, two blue, and two green) are arranged in two rows of three such that no single row or column has two marbles of the same color. How many different arrangements are possible?
a. 12
b. 48
c. 96
d. 128
e. 192 Let’s let the first marble in row 1 be R. We see that one possible layout of the two rows is: RBG BGR Keeping row 1 the same, the only other way to create row 2 is: RBG GRB Now, let’s keep R in first position in row 1; we see that we could now have RGB as row 1. Using a similar strategy as we did above, we see that there are two possible ways to create row 2: either BRG or GBR. We see that when R is in first position of row 1, there are four different marble arrangements that satisfy the stated requirements. Similarly, when G is in first position in row 1, we will obtain four different marble arrangements, and when B is in first position in row 1, we will obtain an additional four different marble arrangements. Thus, the total number of arrangements is 4 + 4 + 4 = 12. Answer: A
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: Six marbles (two red, two blue, and two green) are arranged in two row
[#permalink]
31 May 2018, 16:13






