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Six marbles (two red, two blue, and two green) are arranged in two row

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Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]

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New post 18 May 2018, 00:11
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GST Week 6 Day 3 Veritas Prep Question 3


Give your best shot at writing a top notch explanation and you will have the chance to win GMAT Club tests daily and GMAT On-Demand Prep by Veritas Prep. See the GMAT Spring Training Thread for all details


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

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

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New post 18 May 2018, 00:32
souvik101990 wrote:

GST Week 6 Day 3 Veritas Prep Question 3


Give your best shot at writing a top notch explanation and you will have the chance to win GMAT Club tests daily and GMAT On-Demand Prep by Veritas Prep. See the GMAT Spring Training Thread for all details


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 - G
B - G - R
G - R - B

And

R - B - G
G - 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
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Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]

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New post 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 column
Looking 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:

BRG
RGB

BRG
GBR

RGB
GBR

RGB
BRG

GBR
BRG

GBR
RGB
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Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]

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New post 18 May 2018, 01:12
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souvik101990 wrote:

GST Week 6 Day 3 Veritas Prep Question 3


Give your best shot at writing a top notch explanation and you will have the chance to win GMAT Club tests daily and GMAT On-Demand Prep by Veritas Prep. See the GMAT Spring Training Thread for all details


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 A
similarly F will take 1

total 3*2*1*2*1*1=12
A
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Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]

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New post 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
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Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]

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New post 18 May 2018, 03:55
souvik101990 wrote:

GST Week 6 Day 3 Veritas Prep Question 3


Give your best shot at writing a top notch explanation and you will have the chance to win GMAT Club tests daily and GMAT On-Demand Prep by Veritas Prep. See the GMAT Spring Training Thread for all details


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

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New post 18 May 2018, 04:31
souvik101990 wrote:

GST Week 6 Day 3 Veritas Prep Question 3


Give your best shot at writing a top notch explanation and you will have the chance to win GMAT Club tests daily and GMAT On-Demand Prep by Veritas Prep. See the GMAT Spring Training Thread for all details


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.
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Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]

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New post 18 May 2018, 05:08
3 colors to be place in a row
3! ways
no of rows 2
so 3!x2= 12

A
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Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]

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New post 20 May 2018, 04:06
souvik101990 wrote:

GST Week 6 Day 3 Veritas Prep Question 3


Give your best shot at writing a top notch explanation and you will have the chance to win GMAT Club tests daily and GMAT On-Demand Prep by Veritas Prep. See the GMAT Spring Training Thread for all details


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=2

Now, 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+2-----6 times=12

Please give kudos if it makes sense
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Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]

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New post 28 May 2018, 06:35
souvik101990 wrote:

GST Week 6 Day 3 Veritas Prep Question 3


Give your best shot at writing a top notch explanation and you will have the chance to win GMAT Club tests daily and GMAT On-Demand Prep by Veritas Prep. See the GMAT Spring Training Thread for all details


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



souvik101990
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Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]

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What is the reward for GST - GMAT Spring Training 2018? Is it just the GMAT Club Tests or does the reward include the GMAT On-Demand Prep by Veritas Prep?
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Re: Six marbles (two red, two blue, and two green) are arranged in two row [#permalink]

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New post 30 May 2018, 10:16
Hey houston1980

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If you are the overall winner for the entire week, then you will get the partner award.

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

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New post 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:

R-B-G
B-G-R

Keeping row 1 the same, the only other way to create row 2 is:

R-B-G
G-R-B

Now, let’s keep R in first position in row 1; we see that we could now have R-G-B as row 1. Using a similar strategy as we did above, we see that there are two possible ways to create row 2: either B-R-G or G-B-R.

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