Bane had 3 different color paints with him - Red, Green, and Blu

Question

Bane had 3 different color paints with him - Red, Green, and Blue. He wanted to paint a wall with 6 vertical stripes, but no two adjacent stripes could be of the same color. Assuming that Bane can use one color more than once, in how many ways can Bane paint the wall?

A. 32
B. 64
C. 96
D. 243
E. 729

Thanks,
Saquib
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Official Answer

C

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stonecold · Accepted Answer

Here is what i did in this one ->

Using the rules mentioned in the question STEM->

First strip can be painted with 3 colours.
Second strip can be painted with 2 colours.
Third strip can be painted with 2 colours.
Fourth strip can be painted with 2 colours.
Fifth strip can be painted with 2 colours.
Sixth strip can be painted with 2 colours.

Hence number of ways => 3*2*2*2*2*2=> 3*2^5 => 3*32 => 96 ways.

SMASH THAT C.

EgmatQuantExpert · Answer

Reserving this space to post the official solution.

BrentGMATPrepNow · Answer

Take the task of painting the 6 stripes and break it into   stages  .

Stage 1 : Select a color for the first stripe
Since we have 3 colors to choose from, we can complete stage 1 in  3  ways

Stage 2 : Select a color for the 2nd stripe
This stripe cannot be the same color as stripe #1. 
So, there are 2 remaining colors from which to choose, which means we can complete this stage in  2  ways.

Stage 3 : Select a color for the 3rd stripe
This stripe cannot be the same color as stripe #2. 
So, there are 2 remaining colors from which to choose, which means we can complete this stage in  2  ways.

Stage 4 : Select a color for the 4th stripe
Applying the logic we applied above, we can complete this stage in  2  ways

Stage 5 : Select a color for the 5th stripe
We can complete this stage in  2  ways

Stage 6 : Select a color for the 6th stripe
We can complete this stage in  2  ways.

By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus paint all 6 stripes) in  (3)(2)(2)(2)(2)(2)  ways (= 96 ways)

Answer: C

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Moritz279 · Answer

I believe the problem is formulated wrong.

"Assuming that Bane can use one color more than once, in how many ways can Bane paint the wall"

Sounds for me as if two of the three colors can only paint one stripe so there are always two stripes without any color?

ScottTargetTestPrep · Answer

Solution:
 
For the first stripe, he has 3 choices. For the second stripe, he can use either of the 2 remaining colors (since he can’t repeat colors on adjacent stripes). Similarly, for each of the remaining 4 stripes, he can choose from 2 colors. Thus, for the 6 vertical stripes, he has 3 x 2 x 2 x 2 x 2 x 2 = 96 options.

Answer: C

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Bane had 3 different color paints with him - Red, Green, and Blu

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