GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 Oct 2019, 17:31

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.

Close

Request Expert Reply

Confirm Cancel

Combinatorics/Permutations Fundamental Question

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Theory   
Find Similar Topics 
Intern
Intern
avatar
B
Joined: 06 Aug 2018
Posts: 8
Combinatorics/Permutations Fundamental Question  [#permalink]

Show Tags

New post 25 Aug 2018, 15:11
1
Hello All,

When dealing with permutation questions how do you know when to take the fundamental counting principle approach versus taking the total number of arrangements - unacceptable arrangements?

if we take the example:

There are 6 people, A, B, C, D, E and F. They have to sit around a circular table such that A can sit neither next to D nor next to F. How many such arrangements are possible?

The approach I would take is:

Total arrangements = (6-1)! = 5!

Unacceptable arrangements = AF,FA, DA and AD
= 2*4! + 2*4
= 4*4!

but we have accounted for FAD twice in counting arrangements for FA & AD and the same for DAF. So we need to remove this from our unacceptable arrangements.
= 4*4! - 2*3!

Acceptable arrangements = 5! - (4*4! - 2*3!)
= 120 - (24*4 - 12)
= 120 - (96 - 12)
= 36


But the much simpler approach would be to calculate the following below using the attached diagram

acceptable arrangements = 1*3*1*2*3*2*1
= 36
Attachments

Capture.PNG
Capture.PNG [ 7.81 KiB | Viewed 620 times ]

Senior Manager
Senior Manager
User avatar
D
Joined: 18 Jun 2018
Posts: 262
Re: Combinatorics/Permutations Fundamental Question  [#permalink]

Show Tags

New post 27 Aug 2018, 04:49
1
shadez
Thanks for sharing your approach. Really helpful in solving such type of questions.
GMAT Club Bot
Re: Combinatorics/Permutations Fundamental Question   [#permalink] 27 Aug 2018, 04:49
Display posts from previous: Sort by

Combinatorics/Permutations Fundamental Question

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne