Suppose we have six marbles: 3 blue marbles, 2 red marbles,

Question

Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?

A. 90
B. 180
C. 360
D. 540
E. 720

The OA is B

Source: Magoosh

Scott@TargetTestPrep · Answer

swerve wrote:Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?

A. 90
B. 180
C. 360
D. 540
E. 720

The OA is B

Source: Magoosh

Green marble:
Number of options = 3. (The black cup, the white cup, or the purple cup.)

Red marbles:
Case 1: 1 cup holds both red marbles
Number of options = 3. (The black cup, the white cup, or the purple cup.)
Case 2: 2 cups, each with 1 red marble
From 3 cups, the number of ways to choose 2 cups = 3C2 = (3*2)/(2*1) = 3
Total ways = Case 1 + Case 2 = 3+3 = 6

Blue Marbles:
Case 1: 1 cup holds all 3 blue marbles
Number of options = 3. (The black cup, the white cup, or the purple cup.)
Case 2: 1 cup with 2 blue marbles. another with 1 blue marble
From 3 cups, the number of ways to choose 1 cup to hold 2 blue marbles = 3C1 = 3
From the 2 remaining cups. the number of ways to choose 1 cup to hold the third blue marble = 2C1 = 2
To combine these options, we multiply:
3*2 = 6
Case 3: Each cup holds 1 blue marble
Number of options = 1. (1 blue marble in each cup.)
Total ways = Case 1 + Case 2 + Case 3 = 3+6+1 = 10

To combine our options for each color, we multiply:
3*6*10 = 180

The correct answer is B.

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deloitte247 · Answer

Blue marbles = 3
Red marbles = 2
Green marbles = 1
$$Total\ possible\ combinations=\frac{\left(no.\ of\ marbles\right)\left(no.\ of\ colors\right)}{\Pr oduct\ of\ no.\ of\ colors}$$
$$=\frac{6!\cdot3}{3!\cdot2!\cdot1!}$$
$$=\frac{6\cdot5\cdot4\cdot3!\cdot3}{3!\cdot2!\cdot1!}=\frac{6\cdot5\cdot4\cdot3}{2\cdot1}$$
$$=\frac{360}{2}=180$$

GMATGuruNY · Answer

swerve wrote:Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?

A. 90
B. 180
C. 360
D. 540
E. 720

The OA is B

Source: Magoosh

Green marble:
Number of options = 3. (The black cup, the white cup, or the purple cup.)

Red marbles:
Case 1: 1 cup holds both red marbles
Number of options = 3. (The black cup, the white cup, or the purple cup.)
Case 2: 2 cups, each with 1 red marble
From 3 cups, the number of ways to choose 2 cups = 3C2 = (3*2)/(2*1) = 3
Total ways = Case 1 + Case 2 = 3+3 = 6

Blue Marbles:
Case 1: 1 cup holds all 3 blue marbles
Number of options = 3. (The black cup, the white cup, or the purple cup.)
Case 2: 1 cup with 2 blue marbles. another with 1 blue marble
From 3 cups, the number of ways to choose 1 cup to hold 2 blue marbles = 3C1 = 3
From the 2 remaining cups. the number of ways to choose 1 cup to hold the third blue marble = 2C1 = 2
To combine these options, we multiply:
3*2 = 6
Case 3: Each cup holds 1 blue marble
Number of options = 1. (1 blue marble in each cup.)
Total ways = Case 1 + Case 2 + Case 3 = 3+6+1 = 10

To combine our options for each color, we multiply:
3*6*10 = 180

The correct answer is B.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

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