Seating Arrangement

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

Here's another approach.

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/gmat-counting?id=775