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
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.
FCP is indeed a great method to solve such problems. Could you mention any situations in counting problems where FCP isn't appropriate?