Question

Mr. Schwartz has been hired to paint a row of 7 houses. Each house must be painted red, blue, or green. However, to make it aesthetically pleasing, he doesn’t want any three consecutive houses to be the same color. Find the number of ways he can fulfill his task.

Answer 1

Answer: 192 different ways.

Explanation:

We have 3 colors.

So, for the first house, we can choose between 3 colors.

For the second house, we can choose between 2 (because the color that we chose before can not be chosen again)

For the third house, we have again, 2 colors (because the one we chose in the second house can not be chosen again)

and this goes on until we complete the 7 houses.

Now, the number of possible combinations is equal to the number of options that we have for each house (3 for the first one and 2 for the other 6 houses)

So we have:

C = 3*2^6 = 192