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 Starts Oct 17
Chris Peckover, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Chris Peckover, 100th-Percentile GMAT Scorer

Oct 17 · Chris Peckover
Sat · 11:00 AM to 2:00 PM ET
Oct 20 · Chris Peckover
Tue, Thu · 8:00 to 10:00 PM ET
Oct 25 · Josh Braslow
Sun · 1:00 to 4:00 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
EALiveTeachOnDemand 5 seats left Start anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

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

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

Probability

Expert replies
by Mochad » Mon Apr 02, 2012 11:07 am
Hi,

In how many ways a delegation of 4 students can be selected from a group of 12 if 2 students refuse to be selected at the same time?

My solution was to calculate the nbr of ways 4 students can be selected from 12 (4C12 = 12! / 4!(12-4)! = 450 way) then subtracting it from the nbr of ways in which the 2 students (e.g. A & B) are selected together. The way I solved it was (2C12 = 12! / 2!(12-2)! = 66) but the solution was 2C10 and not 2C12?

Can anybody help me and explain why 2C10 and no 2C10?
Join the discussion
Source: — Problem Solving |

by klmehta03 » Mon Apr 02, 2012 11:45 am
Combinations with restrictions:
with no restrictions= 12C4= 495
with restrictions= (10C2*2C2)
subtraction= 495-45= 450
Join the discussion

by Bill@VeritasPrep » Mon Apr 02, 2012 12:20 pm
Mochad wrote:Hi,

In how many ways a delegation of 4 students can be selected from a group of 12 if 2 students refuse to be selected at the same time?

My solution was to calculate the nbr of ways 4 students can be selected from 12 (4C12 = 12! / 4!(12-4)! = 450 way) then subtracting it from the nbr of ways in which the 2 students (e.g. A & B) are selected together. The way I solved it was (2C12 = 12! / 2!(12-2)! = 66) but the solution was 2C10 and not 2C12?

Can anybody help me and explain why 2C10 and no 2C10?
If we're looking for delegations that include the 2 students, they already take up 2 of the 4 spots. We have 2 remaining spots to fill, and we have 10 students to choose from (since the 2 students who don't like each other are already included).
Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays

Visit the Veritas Prep Blog

Try the FREE Veritas Prep Practice Test
Join the discussion

by Mochad » Mon Apr 02, 2012 2:17 pm
Thank you Bill :) I forgot that we should select 4 and not 2 members!!

BTW what is the difficulty of this question? Is it medium?
Join the discussion