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.

192 different ways.

Step-by-step 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

1875cm³

step-by-step explanation:

we have a 20 × 20 × 5 container with (what im guessing is a) 5 × 5 × 5 hole in the center. first, we need to calculate the volume of the 20 × 20 × 5 container.

20 × 20 × 5 = 2000cm³

now, we need to calculate the volume of the hole.

5 × 5 × 5 = 125cm³

now to find the area of the container, we take to solid area of the container, and subtract the area of the hole.

2000cm³ - 125cm³ = 1875cm³