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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

P&C Problem

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 202
Joined: Sun Sep 08, 2013 11:51 amFollowed by: 2 members
Thanked: 3 times
by sukhman » Thu Sep 12, 2013 8:36 am
Three dwarves and three elves sit down in a row of six chairs. If no dwarf will sit next to another dwarf and no elf will sit next to another elf, in how many different ways can the elves and dwarves sit? Answer [spoiler]6 × 2 × 1 × 3 × 2 × 1 = 72[/spoiler]
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Senior | Next Rank: 100 Posts
Posts: 81
Joined: Tue Jun 11, 2013 10:24 pmFollowed by: 1 member
Thanked: 7 times

by sanjoy18 » Thu Sep 12, 2013 8:45 am
there would be two cases 1) dedede 2) ededed
case 1 & 2 can be done in total 36 ways each
3*3*2*2*1*1=36


hence 36+36 =72
sukhman wrote:Three dwarves and three elves sit down in a row of six chairs. If no dwarf will sit next to another dwarf and no elf will sit next to another elf, in how many different ways can the elves and dwarves sit? Answer [spoiler]6 × 2 × 1 × 3 × 2 × 1 = 72[/spoiler]
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 643
Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members
Thanked: 48 times

by vinay1983 » Thu Sep 12, 2013 9:26 am
The dwarfs and elves have to arranged in alternate manner.

Dwarfs first 3 3 2 2 1 1 so this is "and" arrangement, Hence 36

OR

Elves first 3 3 2 2 1 1 so 36 again

Total 36 or 36 i.e 36+36=72
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

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] » Thu Sep 12, 2013 12:04 pm
Hi sanjoy18 and vinay1983,

You're both absolutely correct. You can save a bit of time though (and avoid the extra calculation), if you think of it this way:

With 3 dwarves and 3 elves, the seating must alternate. With the same number of each, the first "spot" could be either a dwarf or an elf.

So 6 - - - - -

The rest of the pattern proceeds normally...

6 3 2 2 1 1

(6)(3)(2)(2)(1)(1) = 72

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
Post new topic Post Reply
• Page 1 of 1