each face of a cube can be painted either yellow or red. how many different ways can you paint the cube?
10
15
12
To determine the number of different ways the cube can be painted, let's break down the problem step by step.
First, consider one face of the cube. We have two choices for painting it, either yellow or red.
Therefore, there are 2 ways to paint the first face.
For the second face, we again have two choices, yellow or red.
Since there are 2 choices for the first face, and 2 choices for the second face, the total number of ways to paint the first two faces is 2 x 2 = 4.
Now, let's add the third face. Again, we have two choices for each face, so we multiply the previous total by 2. 4 x 2 = 8.
As we proceed to the fourth, fifth, and sixth faces, we continue to multiply the count by 2 since we have 2 choices for each face.
Finally, we have painted all six faces, so the total number of different ways to paint the cube is 2 x 2 x 2 x 2 x 2 x 2 = 64.
Therefore, there are 64 different ways to paint the cube with either yellow or red.