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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
The Carson family will purchase three used cars. There are two models
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15 Apr 2021, 00:50
15 Apr 2021, 00:50
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Question Stats:
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The Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is available in four colors: blue, black, red, and green. How many different combinations of three cars can the Carsons select if all the cars are to be different colors?
A. 24
B. 32
C. 48
D. 60
E. 192
A. 24
B. 32
C. 48
D. 60
E. 192
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Joined: 10 Apr 2015
Posts: 6218
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The Carson family will purchase three used cars. There are two models
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15 Apr 2021, 06:11
15 Apr 2021, 06:11
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GeminiHeat wrote:
The Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is available in four colors: blue, black, red, and green. How many different combinations of three cars can the Carsons select if all the cars are to be different colors?
A. 24
B. 32
C. 48
D. 60
E. 192
A. 24
B. 32
C. 48
D. 60
E. 192
Take the task of selecting cars and break it into stages.
Stage 1: Select 3 different colors.
Since the order in which we select the colors does not matter, we can use combinations.
We can select 3 colors from 4 colors in 4C3 ways (4 ways).
ASIDE: If anyone is interested, we have a video on calculating combinations (like 4C3) in your head (see below)
Stage 2: For one color, choose a model
There are two models (A or B) so this stage can be accomplished in 2 ways.
Stage 3: For another color, choose a model
There are two models (A or B) so this stage can be accomplished in 2 ways.
Stage 4: For the last remaining color, choose a model
There are two models (A or B) so this stage can be accomplished in 2 ways.
By the Fundamental Counting Principle (FCP) we can complete all 4 stages (and thus select the 3 cars) in (4)(2)(2)(2) ways (= 32 ways)
Answer: B
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
General Discussion
Re: The Carson family will purchase three used cars. There are two models
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15 Apr 2021, 03:34
15 Apr 2021, 03:34
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selecting 3 different color cars out of 4 possible colors.= 4! / 3!*1!
each color car has two options: model A or model B which will be 2^3
Therefore, (4! / 3!*1!) * (2^3) = 32 ways.
each color car has two options: model A or model B which will be 2^3
Therefore, (4! / 3!*1!) * (2^3) = 32 ways.
