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 →

COMBINATORICS-2

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members
Thanked: 127 times

by Night reader » Mon Mar 07, 2011 8:59 pm
Is this just 4*4*4 --> total 64 ways?
gmat7202011 wrote:In how many ways can 4 rings be worn on 3 fingers (index finger, middle finger and ring finger), if there is no restriction on the number of rings worn on a finger ?

Thank You
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 423
Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members
Location: Seattle, WA
Thanked: 86 times

by srcc25anu » Mon Mar 07, 2011 9:11 pm
should it not be 3^4 = 81 ways

each ring can be worn in 3 ways. so 4 rings can be worn in 3*3*3*3 = 81 ways
Last edited by srcc25anu on Mon Mar 07, 2011 9:58 pm, edited 2 times in total.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members
Location: Milpitas, CA
Thanked: 1854 times
GMAT Score:770

by Anurag@Gurome » Mon Mar 07, 2011 9:12 pm
I have deleted this post
Last edited by Anurag@Gurome on Mon Mar 07, 2011 9:40 pm, edited 1 time in total.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members
Location: Milpitas, CA
Thanked: 1854 times
GMAT Score:770

by Anurag@Gurome » Mon Mar 07, 2011 9:19 pm
I have deleted this post
Last edited by Anurag@Gurome on Mon Mar 07, 2011 9:41 pm, edited 1 time in total.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members
Thanked: 127 times

by Night reader » Mon Mar 07, 2011 9:33 pm
@Anurag, 1 finger can hold even 0 OR more than 0 ring(s) - to be precise, as there's no restriction per the number of rings on a finger. Otherwise how one finger can hold 4 rings and yet the other will hold something? It's the same as srss25 says one ring to more than 1 finger ...
Anurag@Gurome wrote:
srcc25anu wrote:should it not be 3^4 = 81 ways

each ring can be worn in 3 ways. so 4 rings can be worn in 3*3*3*3 = 81 ways
Each ring cannot be worn in 3 ways, but in only 1 way.
This is because 1 ring cannot go to more than 1 finger.
But, 1 finger can hold more than 1 ring.
So, a finger can be repeated in 4 ways.
Remember, that which can be repeated goes as the power!
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 56
Joined: Sat Dec 11, 2010 2:39 pm
Thanked: 3 times

by gmat7202011 » Mon Mar 07, 2011 10:09 pm
The correct answer is 81.

Thank You all for initiating the discussion, makes me think clearer.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members
Thanked: 127 times

by Night reader » Mon Mar 07, 2011 11:56 pm
@gmat7202011: WHAT'S THE SOURCE OF THIS QUESTION?
@Anurag, why the solution get's deleted?
@srcc25anu, please explain distribution formula 3^4?

Firstly, is this is any GMAT question? Secondly, the problem does not specify if the rings are identical or not. BUT let's assume both cases for now

Identical rings - ORDER does not matter --> 4C3 * 4C3 *4C3 = 4*4*4=64 ways
Rings are Unique - ORDER does matter --> using the formula n!*C(n+r -1, r-1) we get 4!*6C2 = 360 ways

please reveal the SOURCE and not the "correct" answer
gmat7202011 wrote:In how many ways can 4 rings be worn on 3 fingers (index finger, middle finger and ring finger), if there is no restriction on the number of rings worn on a finger ?

Thank You
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 106
Joined: Fri Feb 05, 2010 9:39 amFollowed by: 1 member
Thanked: 4 times

by czarczar » Tue Mar 08, 2011 4:45 am
Night reader wrote:Is this just 4*4*4 --> total 64 ways?
gmat7202011 wrote:In how many ways can 4 rings be worn on 3 fingers (index finger, middle finger and ring finger), if there is no restriction on the number of rings worn on a finger ?

Thank You
I thought that it will be 4_ * _3 * _2
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 613
Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members
Location: madrid
Thanked: 171 times
GMAT Score:790

by kevincanspain » Tue Mar 08, 2011 5:37 am
If identical we have several cases:

4 on one finger- - - - choose one of 3 fingers = 3
3 on one finger, 1 on another---- choose one of 3 fingers to hold 3, another to hold 1 = 6
2 +1 +1- choose one of three fingers to hold 2, the others hold one each = 3
2 + 2 - choose finger to hold none, the others hold two each= 3

Thus 15


If distinct, each of the 4 rings can go on any of the three fingers = 3^4 = 81
Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 56
Joined: Sat Dec 11, 2010 2:39 pm
Thanked: 3 times

by gmat7202011 » Tue Mar 08, 2011 6:30 am
Hi Kevin,

Thank for the response, I guess, we need to consider them distinct rings, since there is no mention of they being identical.

Night Reader,

I ran into this question from a Math Quant book by Arun sharma, i found in a library in Chicago.

Also, "reveal" is a word you use, when you hide something, i guess a better phrase in this context would have been
"Can you please let us know the source of the question ?"


"reveal the source" not the correct answer, i guess mentioning the correct answer is important too.

Thank You
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 613
Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members
Location: madrid
Thanked: 171 times
GMAT Score:790

by kevincanspain » Tue Mar 08, 2011 11:01 am
A GMAT question would probably specify whether they were different or identical, but I thought it would be nice to present a solution for each case. It is, however, nice to disclose/reveal/mention/cite the source, as some people may wish to avoid doing GMATPrep questions until they have used the simulation software by the same name several times
Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 543
Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members
Thanked: 147 times

by anshumishra » Thu Mar 10, 2011 5:40 pm
kevincanspain wrote:If identical we have several cases:

4 on one finger- - - - choose one of 3 fingers = 3
3 on one finger, 1 on another---- choose one of 3 fingers to hold 3, another to hold 1 = 6
2 +1 +1- choose one of three fingers to hold 2, the others hold one each = 3
2 + 2 - choose finger to hold none, the others hold two each= 3

Thus 15


If distinct, each of the 4 rings can go on any of the three fingers = 3^4 = 81
Perfect kevincanspain !

For the identical case, we can also look at the problem in another way which reduces the calculation. We want to distribute 4 things (4 rings) among 3 people (3 fingers here), where each one can receive 0 or more things =
(n+r-1)C(r-1) = (4+3-1)C(3-1)
= 6C2 = 15.
Thanks
Anshu

(Every mistake is a lesson learned )
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1