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Jevan must paint 3 rooms in a house. Room A can be painted o
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19 Nov 2019, 12:08
19 Nov 2019, 12:08
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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, and 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
A. 24
B. 26
C. 27
D. 63
E. 64
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Jevan must paint 3 rooms in a house. Room A can be painted o
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19 Nov 2019, 13:02
19 Nov 2019, 13:02
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huda 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, and 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
A. 24
B. 26
C. 27
D. 63
E. 64
Take the task of painting the 3 rooms and break it into stages.
Stage 1: Select a color for Room A
Room A can be painted orange, red or green
So, we can complete stage 1 in 3 ways
Stage 2: Select a color for Room B
Room B can be painted orange, white or red.
So we can complete this stage in 3 ways.
Stage 3: Select a color for Room C
Room C can be painted white, red or green.
So we can complete this stage in 3 ways.
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus paint all 3 rooms) in (3)(3)(3) ways (= 27 ways)
However, some of these 27 possible outcomes BREAK the condition that the 3 rooms cannot all be painted the same color.
Given the different color options for each room, we can see that the ONLY way that the 3 rooms can be the same color is when all 3 rooms are painted RED.
Since there is only 1 way to BREAK the given condition, the number of GOOD outcomes = 27 - 1 = 26
Answer: B
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
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Re: Jevan must paint 3 rooms in a house. Room A can be painted o
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01 Apr 2024, 18:09
01 Apr 2024, 18:09
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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