Permutations - Order Matters

Question

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.

james12345 · Accepted Answer

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)

https://www.themathpage.com/aPreCalc/per ... ions-2.htm

bb · Answer

Thanks! I added your post to Walker's Sticky: combination-and-probability-references-56486.html

Vyacheslav · Answer

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

Thanks in advance.

WasimAkramKhan · Answer

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

EgmatQuantExpert · Answer

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

shreyagupta1401 · Answer

Hi, can someone share guidance on probability + P&C? Where to start?

bumpbot · Answer

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.

Permutations - Order Matters

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards