Multiple arrangement combinatorics / permutation vs combinat : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 23 Jan 2017, 02:48

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Multiple arrangement combinatorics / permutation vs combinat

Author Message
TAGS:

### Hide Tags

Manager
Joined: 16 Mar 2011
Posts: 177
Followers: 1

Kudos [?]: 37 [0], given: 13

Multiple arrangement combinatorics / permutation vs combinat [#permalink]

### Show Tags

10 Apr 2011, 10:04
00:00

Difficulty:

(N/A)

Question Stats:

50% (01:04) correct 50% (01:21) wrong based on 1 sessions

### HideShow timer Statistics

Hi again,

Im sorry but I'll be needing you guys r help again I am constantly doing something wrong with combinatorics.. I just can't seem to get the difference between a combination and permutation sometimes.. To me, it seems like the same.. For example;

The I Eta Pi fraternity must choose a delegation of three senior members
and two junior members for an annual interfraternity conference. If I Eta Pi
has 12 senior members and 11 junior members, how many different delegations
are possible?

Because the three spots in the delegation are not distinguishable, choosing the seniors is
equivalent to choosing an anagram of three Y's and nine N's, which can be accomplished in
12!/9!x3! = 220 different ways. Since the choices are successive and independent, multiply the numbers: 220 x 55 = 12,100
different delegations are possible.

My thoughts were (and Im constantly doing this wrong over and over again):
If there are 12 seniors and only 3 spots for members it is distinguishable.. Because if one member is selected for the delegation, only 2 seats are left that can be assigned to any of the remaining 11 members and so on.. I really don't understand why this is a combination..

Any help?
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 920
Followers: 14

Kudos [?]: 341 [0], given: 123

Re: Multiple arrangement combinatorics / permutation vs combinat [#permalink]

### Show Tags

10 Apr 2011, 10:28
My thoughts were (and Im constantly doing this wrong over and over again):
If there are 12 seniors and only 3 spots for members it is distinguishable.. Because if one member is selected for the delegation, only 2 seats are left that can be assigned to any of the remaining 11 members and so on.. I really don't understand why this is a combination..

I think you were on right on but did not complete the puzzle.
The number of ways to choose 3 seniors out of 12 is 12 * 11 * 10.
But since this set is going to contain 3! duplicates (this is a combination problem). Total unique ways = 12 * 11 * 10 / 3!

The number of ways to choose 2 juniors out of 11 is 11*10. But since the set is going to contain 2! duplicates. Total unique ways = 11*10/2!

The total unique ways to choose the seniors and juniors is 12 * 11 * 10 * 11 * 10 / 3! 2! or 12100 committees
Manager
Joined: 16 Mar 2011
Posts: 177
Followers: 1

Kudos [?]: 37 [0], given: 13

Re: Multiple arrangement combinatorics / permutation vs combinat [#permalink]

### Show Tags

10 Apr 2011, 10:32
Hi,

thanks for your reply.. It's the second part I just can't seem to get because if you choose 3 out of 12 and you only have 3 spots that can be filled.. Why is it a combination because if either of those 12 take a seat in the delegation then only 11 can still be seated next to the other one eventually leading to 12!/9!

If the 3 are duplicates, why, for example if you have 3 chairs and 7 people, that is not a duplicate.. Either way it also wouldnt matter who sits on what chair out of the 3 people that eventually will take a seat.. But, because if one person takes a seat on the first chair then there are only 2 chair left for 6 people etc. etc.

I think my main problem is that I just can't seem to get the difference behind the logic of these kind of questions.. Most of the time practicing, I end up thinking its a permutation while its a combination
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 920
Followers: 14

Kudos [?]: 341 [1] , given: 123

Re: Multiple arrangement combinatorics / permutation vs combinat [#permalink]

### Show Tags

10 Apr 2011, 11:03
1
KUDOS
I think based on intuition or judgment - identify if you need the "unique" ways or not. If you do then its a "combination" problem. These problems are typically team formation, committees, groups etc. Permutation exercises are passwords, anagrams, order, race etc. in which the digits / subjects when repeated make sense.
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 161

Kudos [?]: 1708 [1] , given: 376

Re: Multiple arrangement combinatorics / permutation vs combinat [#permalink]

### Show Tags

10 Apr 2011, 12:02
1
KUDOS
l0rrie wrote:
Hi,

thanks for your reply.. It's the second part I just can't seem to get because if you choose 3 out of 12 and you only have 3 spots that can be filled.. Why is it a combination because if either of those 12 take a seat in the delegation then only 11 can still be seated next to the other one eventually leading to 12!/9!

If the 3 are duplicates, why, for example if you have 3 chairs and 7 people, that is not a duplicate.. Either way it also wouldnt matter who sits on what chair out of the 3 people that eventually will take a seat.. But, because if one person takes a seat on the first chair then there are only 2 chair left for 6 people etc. etc.

I think my main problem is that I just can't seem to get the difference behind the logic of these kind of questions.. Most of the time practicing, I end up thinking its a permutation while its a combination

I agree with gmat1220.

Permutations:
Arrangement and Order matters.
Let me give you a small example.
How many words can you form with two letters A and B, if the letters can't be repeated.
AB
BA
2 i.e. 2P2 = 2!(Permutation)

How many teams of 2 can you select with two girls A and B.
Can it be
AB
BA
No... AB and BA are both same teams. Order doesn't matter. If AB are used, that should be it.
2C2 = 1(Combination)

I don't get these concepts many times myself. Tell you my trick; I have by heart most of the patterns used in the combinations and permutations. Consequence: when I encounter a really witty question, I just scratch my head and roll my eyes. Then again, not many of the questions are witty.

Say for the above question, I would blindly solve it using combination. I won't even bother to look for alternative approaches. I know there are x people, y needs to be selected: ah.. selected(Combination). I got you Mr question.

3 out of 12 AND 2 out of 11
12C3 * 11C2 (I read it somewhere: AND is multiplication and OR is addition)

If you start with the pattern recognition in these questions like a robot, you will do just fine initially. The interesting part is: after solving many questions, you will automatically start getting the underlying logic behind the solution. Don't ask me how; just try it yourself. But, if you are a guy who just abhors to solve a question without proper visualization; please ignore my suggestion.
_________________
Manager
Joined: 16 Mar 2011
Posts: 177
Followers: 1

Kudos [?]: 37 [0], given: 13

Re: Multiple arrangement combinatorics / permutation vs combinat [#permalink]

### Show Tags

10 Apr 2011, 12:18
Thanks fluke! Pfff, I think most of the times Im really just thinking too practical.. Everytime I get these questions wrong simply because Im trying to make 'sense' out of it.. I did noticed like you and gmat1220 said that the 'selection' questions are combination problems.. However, I get tricked because I think that there is an order when there isn't.. In this question I was thinking, if one seat is taken in the delegation then only 11 are still available to take the seat and it does matter who gets the place.. But am I understanding you correctly that in this case you would say that it doesnt matter in which order the three senior members/junior members are selected? Why is this different then when for example considering seating 7 people in 3 chairs in a row.. I mean, there you're applying the same principle right? I think i'll just try to ignore my overthinking lol and memorize all the forms in which comb/perms can appear.. Soooo annoying this!

Again, thanks everyone!
SVP
Joined: 16 Nov 2010
Posts: 1672
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 33

Kudos [?]: 514 [0], given: 36

Re: Multiple arrangement combinatorics / permutation vs combinat [#permalink]

### Show Tags

10 Apr 2011, 16:57
Three senior members can be chosen in 12C3 ways

Two junior members can be chosen in 11C2 ways

So by principles of counting, total # of ways = 12C3 * 11C2 = (12 * 11 * 10)/(3 * 2) * (11 * 10)/2

= 11 * 10 * 11 * 10

= 12100
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Director
Joined: 01 Feb 2011
Posts: 755
Followers: 14

Kudos [?]: 115 [0], given: 42

Re: Multiple arrangement combinatorics / permutation vs combinat [#permalink]

### Show Tags

24 Apr 2011, 19:10
number of ways of selecting 3 seniors out of 12 = 12c3

number of ways of selecting 2 juniors out of 11 = 11c2

number of ways of selecting 3 seniors and 2 juniors = 12c3*11c2 ( as they both are independent)

=12100
Re: Multiple arrangement combinatorics / permutation vs combinat   [#permalink] 24 Apr 2011, 19:10
Similar topics Replies Last post
Similar
Topics:
Combinatorics 1 13 Oct 2011, 08:21
Combinatorics 2 21 Oct 2010, 13:10
1 Combinatorics choosing from multiple sources without rep. 3 02 Sep 2010, 02:00
1 Combinatorics 6 08 Aug 2010, 14:15
188 Letter arrangements: understanding probability and combinats 39 06 Oct 2009, 13:41
Display posts from previous: Sort by