Find all School-related info fast with the new School-Specific MBA Forum

It is currently 29 Jul 2014, 03:28

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M01 #24

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
VP
VP
avatar
Joined: 05 Mar 2008
Posts: 1477
Followers: 11

Kudos [?]: 193 [0], given: 31

GMAT Tests User
M01 #24 [#permalink] New post 19 Nov 2009, 12:55
1
This post was
BOOKMARKED
Can someone give me an explanation on how to solve these probability in a circle type problems?

The formula is (N-1)! but why?

If 5 noble knights are to be seated at a round table, then how many different ways can they be seated?

120
96
60
35
24

[Reveal] Spoiler:
E
2 KUDOS received
Intern
Intern
avatar
Joined: 10 Jun 2009
Posts: 28
Followers: 0

Kudos [?]: 12 [2] , given: 2

Re: M01 #24 [#permalink] New post 20 Nov 2009, 01:48
2
This post received
KUDOS
Now if we were to arrange them on a bench then we would use following formula n! i.e; 1st position can be taken by any 1 of the 5 knights, 2nd position can be taken by only 1 of the 4 knights because 1 knight has already taken the 1st position, simillarly 3rd position can be taken by any 1 of the 3 knights .......

Thus the formula is = no of ways the 1st position can be filled *no of ways the 2nd position can be filled *no of ways the 3rd position can be filled * no of ways the 4th position can be filled *no of ways the 5th position can be filled = 5*4*3*2*1 = 120

But in circular permutation for distinct objects one has to elliminate all the repeations i.e; we must count all the possibilities only once but we can take both clockwise and anticlockwise as seperate arrangements

Let X,Y,Z,P and Q be the knights

........x
q.............y
p............ z

Here , x y z p q is a possible arrangement (clockwise) and x q p z y is also a possible arrangement (anticlockwise)
But y z p q x or z p q x y or q p z y x etc.. are not distinct arrangements.
Simillarly for ,
......x
p........... z
q........... y

and others

Thus we have the formula (n-1)!, which elliminates all repeatitions.

But for not distinct objects you have only one possible combination i,e; either clockwise or anticlockwise e.g. pearls in a necklace.

Thus we have the formula (n-1)!/2

Hope this helps :-D

Last edited by manojmakkatt on 22 Nov 2009, 07:13, edited 1 time in total.
CIO
CIO
avatar
Joined: 02 Oct 2007
Posts: 1218
Followers: 87

Kudos [?]: 637 [0], given: 334

GMAT ToolKit User GMAT Tests User
Re: M01 #24 [#permalink] New post 20 Nov 2009, 02:20
Hi,
This question has already been discussed here:
m01-q24-78548.html

Please search this thread for the questions that were already discussed:
gmat-club-tests-master-threads-all-tests-78599.html

If you can't find the discussion you need in the thread above, please use Forum Search or Custom Google Search available at the top of every page.

Please do not create duplicate topics. Thank you for cooperation :).
lagomez wrote:
Can someone give me an explanation on how to solve these probability in a circle type problems?

The formula is (N-1)! but why?

If 5 noble knights are to be seated at a round table, then how many different ways can they be seated?

120
96
60
35
24

[Reveal] Spoiler:
E

_________________

Welcome to GMAT Club! :)
Facebook TwitterGoogle+LinkedIn
Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Please read this before posting in GMAT Club Tests forum
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

Get the best GMAT Prep Resources with GMAT Club Premium Membership

VP
VP
avatar
Joined: 05 Mar 2008
Posts: 1477
Followers: 11

Kudos [?]: 193 [0], given: 31

GMAT Tests User
Re: M01 #24 [#permalink] New post 20 Nov 2009, 09:17
manojmakkatt wrote:
Now if we were to arrange them on a bench then we would use following formula n! i.e; 1st position can be taken by any 1 of the 5 knights, 2nd position can be taken by only 1 of the 4 knights because 1 knight has already taken the 1st position, simillarly 3rd position can be taken by any 1 of the 3 knights .......

Thus the formula is = no of ways the 1st position can be filled *no of ways the 2nd position can be filled *no of ways the 3rd position can be filled * no of ways the 4th position can be filled *no of ways the 5th position can be filled = 5*4*3*2*1 = 120

But in circular permutation for distinct objects one has to elliminate all the repeations i.e; we must count all the possibilities only once but we can take both clockwise and anticlockwise as seperate arrangements

Let X,Y,Z,P and Q be the knights

........x
q.............y
p............ z

Here , x y z p q is a possible arrangement (clockwise) and x q p z y is also a possible arrangement (anticlockwise)
But y z p q x or z p q x y or q p z y x etc.. are not distinct arrangements.
Simillarly for ,
......x
p........... z
q........... y

and others

Thus we have the formula (n-1)!, which elliminates all repeatitions.

But for not distinct objects you have only one possible combination i,e; either clockwise or anticlockwise e.g. pearls in a necklace.

Thus we have the formula (n-1)!/2

Hope this helps :-D


thanks for the explanation
Re: M01 #24   [#permalink] 20 Nov 2009, 09:17
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic M01, Q24 sunman 2 29 Dec 2011, 14:55
1 m01 q24 sfeiner 6 24 Dec 2009, 13:24
M01Q24 DenisSh 1 06 Sep 2009, 23:27
M01 Q24 ThrillRide 2 07 Jul 2009, 06:26
Experts publish their posts in the topic m01-q24 pmal04 9 16 May 2009, 06:39
Display posts from previous: Sort by

M01 #24

  Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: Bunuel, WoundedTiger



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.