Question

Jevan must paint 3 rooms in a house.Room A can be painted orange,red or green.Room B can be painted orange,white or red.Room C can be painted white,red or green.The 3 rooms cannot all be painted the same color.In how many different ways could Jevan paint the 3 rooms?

1) 24
2) 26
3) 27
4) 63
5) 64

Answer 1

2) 26

Explanation:

The first thing to paint is to divide it into three parts, like this:

1st part:

Room A can be painted orange, red or green.

Therefore, we have 3 ways to do it.

2nd part:

Room B can be painted orange, white or red.

Therefore, we have 3 ways to do it.

3rd part:

Room C can be painted white, red or green.

Therefore, we have 3 ways to do it.

To know the total number, each part must be multiplied, that is:

3 * 3 * 3 = 27

However, some of these 27 possible results break the condition that the 3 rooms cannot be painted the same color, that only happens when the three rooms are painted red.

Therefore, the number of times would be:

27 - 1 = 26