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Without restriction, since each room can be painted in 3 ways, the total number of ways to paint the rooms is 3^3.BTGmoderatorDC wrote: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
OA B
Source: Magoosh
Take the task of painting the 3 rooms and break it into stages.BTGmoderatorDC wrote: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?
A) 24
B) 26
C) 27
D) 63
E) 64
If there were no restrictions, there would be 3 x 3 x 3 = 27 ways to paint the 3 rooms. The only way they could be painted the same color would be if they were all painted red. Therefore, there are 27 - 1 = 26 ways to paint the 3 rooms such that all three rooms are not painted the same color.BTGmoderatorDC wrote: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
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