Problem Solving

E-GMAT

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

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?

Let Bane paint the first stripe
Three colors are available for the first stripe, so he can paint the first stripe in 3 ways.

Now, for the second stripe he has only two colors avilable as he can not paint the second stripe with the same color as the color of the first stripe. So, he can paint the second stripe in 2 ways.

Similarly, for third stripe, 2 ways
For fourth stripe, 2 ways
For fifth stripe, 2 ways
For sixth stripe, 2 ways

Total no. of ways = 3 * 2 * 2 * 2 * 2 * 2 = 96

Option C is the answer.