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There are six different models that are to appear in a fashion show. T
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06 Oct 2021, 09:13
06 Oct 2021, 09:13
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There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
A. 72
B. 48
C. 64
D. 24
E. 8
A. 72
B. 48
C. 64
D. 24
E. 8
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Re: There are six different models that are to appear in a fashion show. T
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06 Oct 2021, 09:25
06 Oct 2021, 09:25
1
Carcass wrote:
There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
A. 72
B. 48
C. 64
D. 24
E. 8
A. 72
B. 48
C. 64
D. 24
E. 8
Take the task of arranging the models and break it into stages.
Stage 1: Select a model to stand in position #1
There are 6 models to choose from, so we can accomplish this stage in 6 ways.
Stage 2: Select a model to stand in position #2
Since models from the same country must stand together, there's only 1 model who can stand in position #2
So, we can complete this stage in 1 way
Stage 3: Select a model to stand in position #3
There are 4 models remaining, so we can accomplish this stage in 4 ways.
Stage 4: Select a model to stand in position #4
Since models from the same country must stand together, there's only 1 way to complete this stage
Stage 5: Select a model to stand in position #5
There are 2 models remaining, so we can accomplish this stage in 2 ways.
Stage 6: Select a model to stand in position #6
There is only 1 model remaining, so we can accomplish this stage in 1 way.
By the Fundamental Counting Principle (FCP) we can complete all 6 stages (and thus arrange all 6 models) in (6)(1)(4)(1)(2)(1) ways (= 48 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.
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Re: There are six different models that are to appear in a fashion show. T [#permalink]
06 Oct 2021, 09:25
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