Bane had 3 different color paints with him - Red, Green, and Blue. He wanted to paint a wall with 6 vertical stripes,

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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


OA C

Source: e-GMAT

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BTGmoderatorDC wrote:
Mon Aug 08, 2022 10:55 pm
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


OA C

Source: e-GMAT
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.
Brent Hanneson - Creator of GMATPrepNow.com
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