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 →

PandC

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 462
Joined: Wed Jan 19, 2011 1:08 pmFollowed by: 4 members
Thanked: 10 times
by confuse mind » Sat Jul 21, 2012 7:43 pm
There are 6 boxes numbered 1, 2 ...6. Each box is to be filled up either with a red or a green ball in such a way
that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The
total number of ways in which this can be done is
A. 5
B. 21
C. 33
D. 60
E. 6


Please give your complete solution
IMO - B
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 520
Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members
Thanked: 339 times
GMAT Score:770

by eagleeye » Sat Jul 21, 2012 9:57 pm
confuse mind wrote:There are 6 boxes numbered 1, 2 ...6. Each box is to be filled up either with a red or a green ball in such a way
that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The
total number of ways in which this can be done is
Please give your complete solution
IMO - B
We need to find in how many ways can we have green balls in the 6 boxes when the green balls are together. The inherent assumption here is that the balls are identical. With that in mind, let's figure this one out:

Case 1: Only one green ball. The green ball can occupy any of the 6 boxes. No. of ways = 6.

Case 2: Two green balls together (consecutively numbered boxes means that the balls are always together). Think of the 2 balls as a single entity, then we can have 5 position for the twin arrangement. (for the remaining 4 boxes, we have _ R _ R _ R _ R _, where the two green boxes can be anywhere in the 5 spaces shown among the 4 red balls in boxes. No of ways = 5.

Case 3: Three balls together, 4 spaces. No. of ways = 4.

In the same way, we get for the other 3 cases 3, 2, 1.

Hence total number of ways = 6+5+4+3+2+1 = 21.
B is correct.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1