distinguish perm/comb : GMAT Quantitative Section
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 28 Feb 2017, 02:12

### 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

# distinguish perm/comb

Author Message
TAGS:

### Hide Tags

Manager
Joined: 08 Sep 2010
Posts: 58
Followers: 0

Kudos [?]: 27 [0], given: 4

### Show Tags

08 Nov 2011, 14:14
Hi guys, having a little trouble distinguishing the two.

Comb = unordered where order doesen't matter.
perm = order matters.

But, look at this questions:
Question wrote:
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

To me, the second part of the question looks like a perm. Since there are 2 seats and therefore 2 candidates (hence they are distinguishable) wouldn't it be 10!/8!=90?

I know I am wrong. Can someone clarify how I can make a better decision distinguishing the two.

Look at another one:
Quote:
The principal of a high school needs to schedule observations of 6 teachers. she plans to visit one teacher each day for a work week (M-F) so will only have time to see 5 of the teachers. How many different observation schedules can she create?

To me there is no order here as the principal can meet any of the 5 teachers any day! The order in which she meets those "5" selected teachers does not matter. Hence, shouldnt this be a combination problem?

Am I missing some key rule here? or am I just losing it!

Thanks,
Manager
Status: SC SC SC SC SC.... Concentrating on SC alone.
Joined: 20 Dec 2010
Posts: 240
Location: India
Concentration: General Management
GMAT Date: 12-30-2011
Followers: 3

Kudos [?]: 60 [0], given: 47

### Show Tags

08 Nov 2011, 19:33
Keep this rule and example in mind. You wont get confused.

Permutation - order matters - bigger value - so ABC, ACB, BAC, BCA, CAB, CBA all count in the final answer.

Combination - order doesnt matter - small value - so ABC = ACB = BCA = BAC = CAB = CBA = Considered as one value. Account as 1 value.

Second question is a permutation problem.

Bcos the order matters. Every different order count to a particular schedule.
So 6 * 5 * 4 * 3 * 2 is the answer for q2.
_________________

D- Day December 30 2011. Hoping for the happiest new year celebrations !

Aiming for 700+

Kudo me if the post is worth it

Manager
Status: SC SC SC SC SC.... Concentrating on SC alone.
Joined: 20 Dec 2010
Posts: 240
Location: India
Concentration: General Management
GMAT Date: 12-30-2011
Followers: 3

Kudos [?]: 60 [0], given: 47

### Show Tags

08 Nov 2011, 19:47
And the first problem.

Totally we are asked to count the possible positions for set of 3 vaccancies.

1 in math dept, for which we have 7 choices.
2 positions in CSE dept. Identical positions. So one cannot occupy 2 positions and also the order doesn't matter. i.e AB = BA = 1 position. If there is a distinction between two positions then we can classify them as 2 different items. Since they are identical it is considered as 1 position. So it is a combination problem.

So for the 2 positions in CSE dept the possibilities are 10 * 9 / 2 = 45.
Taking them together 7*45 = 315.

Hope it helps
_________________

D- Day December 30 2011. Hoping for the happiest new year celebrations !

Aiming for 700+

Kudo me if the post is worth it

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7194
Location: Pune, India
Followers: 2175

Kudos [?]: 14059 [1] , given: 222

### Show Tags

09 Nov 2011, 03:46
1
KUDOS
Expert's post
386390 wrote:
Hi guys, having a little trouble distinguishing the two.

Comb = unordered where order doesen't matter.
perm = order matters.

Combination is 'selection/picking people out of a group'
Permutation is 'arrangement'

Try using the terms selection and arrangement.

But, look at this questions:
Question wrote:
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

To me, the second part of the question looks like a perm. Since there are 2 seats and therefore 2 candidates (hence they are distinguishable) wouldn't it be 10!/8!=90?

We are given that the 2 seats are identical i.e. you just need to select 2 people. You don't have two different positions (e.g. a professor and an assistant professor). The positions are identical so there is no arrangement here. If the positions were not identical, then we would select two people (e.g. Mr A and Mr. B) and then arrange the two people in the two positions i.e. Mr A is professor and Mr. B is assistant professor OR Mr A is assistant professor and Mr B is professor. We would have 2 different arrangements in that case. That would have been a permutation. Right now, since the two positions are exactly the same, you only have to select two people. This is just a combination.

I know I am wrong. Can someone clarify how I can make a better decision distinguishing the two.

Look at another one:
Quote:
The principal of a high school needs to schedule observations of 6 teachers. she plans to visit one teacher each day for a work week (M-F) so will only have time to see 5 of the teachers. How many different observation schedules can she create?

To me there is no order here as the principal can meet any of the 5 teachers any day! The order in which she meets those "5" selected teachers does not matter. Hence, shouldnt this be a combination problem?

Am I missing some key rule here? or am I just losing it!

Focus on the question - always. It asks you the number of different schedules she can make. Are the following 2 schedules different or not?
Mon - Mr A
Tue - Mr B
Wed - Mr C
Thu - Mr D
Fri - Mr E

and

Mon - Mr E
Tue - Mr A
Wed - Mr C
Thu - Mr D
Fri - Mr B

I hope you agree that the two schedules are different. So here, you choose 5 people out of 6 and then arrange the 5 on 5 different days. Let's say, I chose Mr A, B, C, D and E. Now I need to arrange them on Mon, Tue, Wed, Thu and Fri. Hence we need to choose and arrange here. This is a permutation.

Thanks,

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Re: distinguish perm/comb   [#permalink] 09 Nov 2011, 03:46
Similar topics Replies Last post
Similar
Topics:
3 Distinguish b/w a permutation problem and a combination problem. 6 13 Mar 2015, 04:38
Need help understanding what method to tackle Perm/Comb ques 3 10 Dec 2013, 01:09
Display posts from previous: Sort by