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 →

a rare on GMAT

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members
Location: India
Thanked: 267 times
GMAT Score:760
by sanju09 » Tue Mar 02, 2010 4:22 am
10 different books and 2 different pens are given to 3 boys so that each boy gets equal number of things. What is the probability that same boy doesn't receive both pens?
(A) 3/11
(B) ¼
(C) 4/11
(D) 8/11
(E) 9/11
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 189
Joined: Thu Apr 03, 2008 2:03 pm
Location: USA
Thanked: 21 times

by rohan_vus » Tue Mar 02, 2010 4:38 am
Probability that one boy receives both pens is 10c2*2c2/12c4 = 1/11
So total probability that among 3 boys, anyone will have boths pens, is 3*1/11 = 3/11

So probability that none will have both pens = 1 - 3/11 = 8/11
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Wed Feb 03, 2010 12:09 am
GMAT Score:540

by stufigol » Wed Mar 03, 2010 12:13 am
u explain the 10c2 and 12c4 plz
thanks
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members
Location: India
Thanked: 64 times
GMAT Score:760

by harsh.champ » Wed Mar 03, 2010 4:27 am
stufigol wrote:u explain the 10c2 and 12c4 plz
thanks
Ok.
Lets look at rohan's explanation.
Probability that one boy receives both pens is 10c2*2c2/12c4 = 1/11
So total probability that among 3 boys, anyone will have boths pens, is 3*1/11 = 3/11

So probability that none will have both pens = 1 - 3/11 = 8/11
Suppose the same boy gets both the pens.
Now,10C2 = No. of ways in which the 2 books can be selected.
12C4 = Selection of any 4 items out of the (10 + 2) items

Also,the boy can be selected in 3C1 ways.
So, we have our case (10C2 x 2C2 x 3C1)/12c4 = 3/11
Now, P(favorable case) = 1 - P(all the unfavorable cases)

I hope it is clear now. :)
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1