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Jevan must paint 3 rooms in a house.Room can be painted orange,red or

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Jevan must paint 3 rooms in a house.Room can be painted orange,red or  [#permalink]

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New post 02 Jun 2018, 05:50
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Difficulty:

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Question Stats:

61% (02:04) correct 39% (02:08) wrong based on 71 sessions

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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.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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Re: Jevan must paint 3 rooms in a house.Room can be painted orange,red or  [#permalink]

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New post 02 Jun 2018, 06:16
Room A - Red, Orange, Green
Room B - Red, Orange, White
Room C - Red, Green, White

Total possible combinations = 3*3*3 = 27
Undesired combination = All rooms painted same color, here in our case only one possibility, Red color = 1
Desired possible combinations = 27-1 = 26
Hence, imo option 2


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Sharan Salem
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Re: Jevan must paint 3 rooms in a house.Room can be painted orange,red or  [#permalink]

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New post 02 Jun 2018, 06:20
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Princ 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


Room A - Orange, Red or Green
Room B - Orange, White or Red
Room C - White, Red or Green

# ways to paint Room A = 3 ways
# ways to paint Room B = 3 ways
# ways to paint Room C = 3 ways

Total # ways the three rooms can be painted without any conditions = 3*3*3 = 27 ways

Now the condition that the three rooms will have the same color, is when all three are painted Red. It can be done in only 1 way.

Hence the Total # ways the 3 rooms can be painted = 27-1 = 26 ways.

Answer B.

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GyM
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Re: Jevan must paint 3 rooms in a house.Room can be painted orange,red or  [#permalink]

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New post 01 Oct 2018, 08:44
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Princ 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


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 GMAT. So, be sure to learn it.

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Re: Jevan must paint 3 rooms in a house.Room can be painted orange,red or &nbs [#permalink] 01 Oct 2018, 08:44
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