MathRevolution wrote:

There are 5 couples. If they will sit 10 chairs in a row such that each couple sits side by side, how many possible cases are there?

A. 120

B. 240

C. 1,200

D. 2,460

E. 3,840

*An answer will be posted in 2 days.

Here's one approach:

Take the task of seating the 10 people and break it into

stages.

Stage 1: Select someone to sit in the 1st chair

There are 10 people to choose from, so we can complete stage 1 in

10 ways

Stage 2: Select someone to sit in the 2nd chair

The person seated in the 2nd chair must be the partner of the person in the 1st chair

So we can complete this stage in

1 way.

Stage 3: Select someone to sit in the 3rd chair

There are 8 people remaining. So, we can complete stage 3 in

8 ways

Stage 4: Select someone to sit in the 4th chair

The person seated in the 4th chair must be the partner of the person in the 3rd chair

So, we can complete this stage in

1 way.

Stage 5: Select someone to sit in the 5th chair

There are 6 people remaining. So, we can complete stage 5 in

6 ways

Stage 6: Select someone to sit in the 6th chair

The person seated in the 6th chair must be the partner of the person in the 5th chair

So, we can complete this stage in

1 way.

Stage 7: Select someone to sit in the 7th chair

There are 4 people remaining. So, we can complete stage 7 in

4 ways

Stage 8: Select someone to sit in the 8th chair

The person seated in the 8th chair must be the partner of the person in the 7th chair

So, we can complete this stage in

1 way.

Stage 9: Select someone to sit in the 9th chair

There are 2 people remaining. So, we can complete stage 9 in

2 ways

Stage 10: Select someone to sit in the 10th chair

One 1 person remains.

So, we can complete this stage in

1 way.

By the Fundamental Counting Principle (FCP), we can complete all 10 stages (and thus seat all 10 people) in

(10)(1)(8)(1)(6)(1)(4)(1)(2)(1) ways ([spoiler]= 3840 ways[/spoiler])

Answer:

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Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video:

http://www.gmatprepnow.com/module/gmat-counting/video/775You can also watch a demonstration of the FCP in action:

https://www.gmatprepnow.com/module/gmat ... /video/776Cheers,

Brent

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