Problem Solving

Hi M7MBA,

We're told that 8 dogs are in a pen and the owner lets five dogs out of the pen (one at a time). We're asked for the number of different variations in the line of dogs leaving the pen. This question is a fairly standard version of a Permutation question, so you would probably find it easiest to just write out the numbers and do whatever calculations are necessary.

Since we have 8 dogs and we're going to deal with 5 of them (one at a time - in a line), there would be....
8 options for the 1st dog
7 options for the 2nd dog
6 options for the 3rd dog
5 options for the 4th dog
4 options for the 5th dog

(8)(7)(6)(5)(4) total options

While you could calculate the exact result, the answer choices are 'spaced out' enough that you can estimate that calculation....
(8x7) = about 60
(6x5) = 30
(60)(30) = 1800 and THEN you still have to multiply by 4...
(1800)(4) = about 7000
There's only one answer that's close...

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

M7MBA wrote:Eight dogs are in a pen when the owner comes to walk some of them. The owner lets five dogs out of the pen one at a time. How many different variations in the line of dogs leaving the pen are possible?

A. 6,720
B. 3,360
C. 1,680
D. 560
E. 56

Take the task of arranging the 5 dogs in a line and break it into stages.

Stage 1: Select a dog to be 1st in the line
There are 8 dogs to choose from, so, we can complete stage 1 in 8 ways

Stage 2: Select a dog to be 2nd in the line
There are 7 remaining dogs from which to choose, so we can complete this stage in 7 ways.

Stage 3: Select a dog to be 3rd in the line
There are 6 remaining dogs from which to choose, so we can complete this stage in 6 ways.

Stage 4: Select a dog to be 4th in the line
There are 5 remaining dogs from which to choose, so we can complete this stage in 5 ways.

Stage 5: Select a dog to be 5th in the line
There are 4 remaining dogs from which to choose, so we can complete this stage in 4 ways.

By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus arrange 5 dogs in a line) in (8)(7)(6)(5)(4) ways (= 6720 ways)

Answer: A
--------------------------

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: https://www.gmatprepnow.com/module/gmat- ... /video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent