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) 48
B) 64
C) 24
D) 8
E) 72
OA: A
Seating Arrangement
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Here we have two characteristics that can be separated. First, we have six ways to arrange the continents (NA, SA, Eur).
For each of these six configurations, there are two ways to sort the models (eg NA1, NA2) for each of 3 continents.
So we have 6 continent orders * (2^3) = 6 * 8 = 48
An analogous problem would be:
There are 3 different coins. How many different piles can you make (using both order of the coins and heads/tails positioning)?
For each of these six configurations, there are two ways to sort the models (eg NA1, NA2) for each of 3 continents.
So we have 6 continent orders * (2^3) = 6 * 8 = 48
An analogous problem would be:
There are 3 different coins. How many different piles can you make (using both order of the coins and heads/tails positioning)?

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Firstly, Lets forget about the number of models for now[Since we need to group the models from the same continent]. We have representations from 3 continents[SA, NA, EU]. These 3 representations can be arranged in 3! = 6 Ways.srcc25anu 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) 48
B) 64
C) 24
D) 8
E) 72
OA: A
Now each representation[SA/NA/EU] has two models, who can be arranged in 2! = 2 Ways.
So, in sum, the total number of ways the models can be arranged: 3!*2!*2!*2! = 6*2*2*2 = 48 ways.
Hence the correct answer is [spoiler]No Points for guessing now... [/spoiler]
Hope this helps...
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Here's another approach.srcc25anu 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) 48
B) 64
C) 24
D) 8
E) 72
OA: A
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 ([spoiler]= 48 ways[/spoiler])
Answer is A
Cheers,
Brent
Aside: For more information about the FCP, we have a free video on the subject: https://www.gmatprepnow.com/module/gmatcounting?id=775