Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 21 Jul 2019, 06:43

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

Permutations - Order Matters

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 25 May 2009
Posts: 127
Concentration: Finance
GMAT Date: 12-16-2011
Permutations - Order Matters  [#permalink]

Show Tags

New post 14 Jun 2009, 12:17
10
9
I was struggling with when to use the permutation formula and when to use the combination formula in various problems. The definitions of permutations and combinations are are sometimes not clear to beginners. The easiest way that I have found to use the permutation formula is when the question states that order matters. Looking for key words in the sentence like:
*Rank
*Arrange
*Place
*Chose
*Pick
and many others signify that order matters. If order matters then use the permutation formula.

Examples:

*In how many ways can 8 CD’s be arranged on a shelf?

*If a softball league has 10 teams, how many different end of the season rankings are possible? (Assume no ties).

*How many different arrangements can be made using two of the letters of the word TEXAS if no letter is to be used more than once?

* A teacher has 15 students and 5 are to be chosen to give demonstrations. How many different ways can the teacher choose the demonstrators given the following conditions.

*In how many ways can a sorority of 20 members select a president, vice president and treasury, assuming that the same person cannot hold more than one office.

All of these questions are answered using the permutation formula: \(nPr=\frac{n!}{(n-r)!}\)

This is something that has helped me, hopefully it helps others.
Founder
Founder
User avatar
V
Joined: 04 Dec 2002
Posts: 17846
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
GMAT ToolKit User Premium Member CAT Tests
Re: Permutations - Order Matters  [#permalink]

Show Tags

New post 14 Jun 2009, 16:06
Thanks!
I added your post to Walker's Sticky: combination-and-probability-references-56486.html
_________________
Founder of GMAT Club

Just starting out with GMAT? Start here...
New! OG2020 Directory !
Want to know application stats & Profiles from last year? Check the Decision Tracker

Image
Intern
Intern
avatar
Joined: 25 Oct 2009
Posts: 20
Schools: Wharton, HBS, Stanford
Re: Permutations - Order Matters  [#permalink]

Show Tags

New post 25 Oct 2009, 19:34
3
I3igDmsu wrote:
* A teacher has 15 students and 5 are to be chosen to give demonstrations. How many different ways can the teacher choose the demonstrators given the following conditions.


I think that in this example order doesn't matter. Could somebody prove/reject, pls

Thanks in advance.
_________________
KUDOS if you find it helpful ;)
Intern
Intern
avatar
Joined: 25 Nov 2009
Posts: 15
Location: San Francisco
Schools: Wharton West eMBA, Haas EW, Haas eMBA
Re: Permutations - Order Matters  [#permalink]

Show Tags

New post 03 Jan 2010, 10:06
5
My 2 cents is that this forum is a fantastic way to find resources and hone skills and an awful way to try to gander basic concepts from others' posts. I blundered around not really understanding Permutations and such until reading this link (which certainly came from someone in here who I would give credit to if I could)

http://www.themathpage.com/aPreCalc/per ... ions-2.htm
Intern
Intern
avatar
Joined: 06 Dec 2013
Posts: 1
Re: Permutations - Order Matters  [#permalink]

Show Tags

New post 07 Dec 2013, 06:21
Vyacheslav wrote:
I3igDmsu wrote:
* A teacher has 15 students and 5 are to be chosen to give demonstrations. How many different ways can the teacher choose the demonstrators given the following conditions.


I think that in this example order doesn't matter. Could somebody prove/reject, pls

Thanks in advance.



yes order has no work... only combination is req..
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 2943
Permutations - Order Matters  [#permalink]

Show Tags

New post 05 Jan 2015, 22:50
2
2
WasimAkramKhan wrote:
Vyacheslav wrote:
I3igDmsu wrote:
* A teacher has 15 students and 5 are to be chosen to give demonstrations. How many different ways can the teacher choose the demonstrators given the following conditions.


I think that in this example order doesn't matter. Could somebody prove/reject, pls

Thanks in advance.



yes order has no work... only combination is req..


I3igDmsu has done a great job of giving sample questions where Order Matters :)

He is right that being aware of certain keywords helps you determine whether Order Matters in a question or not. However, please note that the words 'Pick' and 'Choose' indicate that order DOES NOT matter. So, the list of keywords provided by I3igDmsu needs to be corrected in this regard.

This also probably explains why WasimAkramKhan asked the follow-up question, which had the keyword 'choose'. In this question, order DOES NOT matter. It is therefore a selection (combination) question.


- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

While the keywords present in the question statement are of help in clearing the doubt about whether Order Matters or not, nothing beats conceptual understanding of WHY order matters in a particular case and not in another.

Let us try to answer this 'WHY' in the question quoted by WasimAkramKhan above.

Let the 15 students in question be named A, B, C . . . O

The question here asks, in how many ways can the teacher choose the 5 demonstrators?

So, what can the possible groups of demonstrators be?

Some examples are: (ABCDE), (ABCDF) . . . (BCDEO) etc.

Essentially, we are choosing 5 students out of 15 students here and giving them the label of 'demonstrators'. So, this is a SELECTION question. Order doesn't matter here. The answer will be 15C5

This question also illustrates what we said above: The word 'CHOOSE' indicates that the given question involves Selection (Combination) and that Order doesn't matter.

Let us now consider a different question:

A teacher has 15 students and 5 are to be chosen to give demonstrations. In how many ways can the demonstrations be made?

Do you see the difference between this question and the previous one? ('ways to choose the demonstrators' v/s 'ways to make the demonstrations')

In the second question, we will have two tasks to perform:
1. Select a group of 5 students to demonstrate
2. Within a selected group of students, decide the order in which the students make the demonstrations.

For example, let the chosen group of demonstrators be: A, B, C, D and E

Now, within this group, we will have to make another decision: Who will demonstrate first of all? Who will be the second to demonstrate and so on . . .

Basically, ORDER MATTERS in this case. So, this is a Permutation question and the answer to this question will be: 15P5

The Takeaways from this discussion:
When in doubt about whether the given question is about Permutation or about Combination,
1. Look for certain helpful keywords
2. Try to imagine the scenario given in the question (maybe with the help of an example) and ask yourself: DOES ORDER MATTER here?


Hope this helps! :-D

Japinder
_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11719
Re: Permutations - Order Matters  [#permalink]

Show Tags

New post 21 Aug 2018, 10:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: Permutations - Order Matters   [#permalink] 21 Aug 2018, 10:54
Display posts from previous: Sort by

Permutations - Order Matters

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





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