BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Eight dogs are in a pen when the owner comes to walk some

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2058
Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members
Thanked: 1 times
by M7MBA » Sun Feb 18, 2018 4:56 am
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

The OA is the option A.

Is there a fast and easy way to solve this PS question? Experts, may you show me how you'd solve it? Thanks in advanced.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Sun Feb 18, 2018 10:34 am
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
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Thu Feb 22, 2018 8:42 am
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
We are given that there are 8 dogs and the owner needs to arrange 5 of them. Since we have an "ordered arrangement," order matters. So we have a permutation problem. Thus, the number of ways to arrange 5 dogs from 8 is:

8P5 = 8!/(8 - 5)! = 8!/3! = 8 x 7 x 6 x 5 x 4 = 6,720

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Thu Feb 22, 2018 9:33 am
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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1