Live GMAT classes with Target Test Prep start Nov 21 and Nov 22. First class free.

See classes
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.

Newsweek Readers’ Choice Awards 2026 winner: Target Test Prep, #1 Test Prep

Target Test Prep was voted #1 Best Test Prep in the 2026 Newsweek Readers’ Choice™ Awards.

★★★★★5.0563 reviews
GMATLiveTeachStarts Nov 22
Josh Braslow, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Josh Braslow, 20+ years in test prep

Nov 22 · Josh Braslow
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemandStart anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

EXECUTIVE ASSESSMENT

with

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
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 Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemandStart 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 563 reviewsTarget Test Prep

probability problem with condition

Expert replies
Post new topic Post Reply
Subscribe topic
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 43
Joined: Wed Jan 21, 2009 2:24 pm
Thanked: 1 times
by r_walid » Sun Nov 15, 2009 12:32 pm
out of 7 models, 5 will be selected for a photo. if the 5 models are to stand in a line from shortest to tallest and if all are of different heights, and if the fourth and sixth tallest models cannot sit side by side, how many different arrangements of 5 models are possible?

6
11
17
72
210

Please explain with DETAIL your reasoning.
Top
Join the discussion
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 199
Joined: Sat Oct 24, 2009 4:43 pm
Thanked: 22 times
GMAT Score:710

by palvarez » Mon Nov 16, 2009 11:21 am
7c5 = 21 ways without any restrictions.

4 and 6 can't sit side by side, meaning that whenever 4 and 6 are present, we need 5.

Find ways where 4 and 6 are present, but not 5: 4c3 ways = 4

21 - 4 = 17.
Top
Join the discussion
Senior | Next Rank: 100 Posts
Posts: 95
Joined: Thu Mar 12, 2009 2:39 am
GMAT Score:620

by gmat620 » Wed Nov 18, 2009 9:32 pm
good explanation by palvarez !!
Top
Join the discussion
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Thu Nov 26, 2009 6:51 am

by Birgit Anne » Mon Nov 30, 2009 11:41 am
I do not understand your last step:

If Model #6 and Model #4 are selected, but Model #5 is not, why is this 4C3?

Is it because there are 4 models left and three of them have to be choosen in order to have a total of 5 models selected?
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 199
Joined: Sat Oct 24, 2009 4:43 pm
Thanked: 22 times
GMAT Score:710

by palvarez » Mon Nov 30, 2009 11:49 am
Birgit Anne wrote:I do not understand your last step:

If Model #6 and Model #4 are selected, but Model #5 is not, why is this 4C3?

Is it because there are 4 models left and three of them have to be choosen in order to have a total of 5 models selected?
Yes, 4 left off of 7: 4 and 6 are pre-selected, we dont wanna select 5. so, we are left with remaining 4.

Since we preselected 2, we need to pick remaning 3 from above 4.
Top
Join the discussion