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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A three-person committee must be chosen from a group of 7 [#permalink]

Show Tags

26 May 2012, 11:58

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

73% (02:49) correct
27% (02:13) wrong based on 170 sessions

HideShow timer Statistics

Hi All,

Need help to understand what is wrong with my approach.

A three-person committee must be chosen from a group of 7 professors and 10 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?

A. 70 B. 560 C. 630 D. 1,260 E. 1,980

My approach :- There are 3 seats. One has to be a professor. The remaining can be occupied by remaining professors or students.

Thus ways of filling seat 1 is 7 (You have to pick one professor out of 7) Ways of filling remaining 2 seats will be to pick 2 out of 16 (10 S and 6 P as one P has already been picked. ) i.e. C(16,2) = 16*15/2 = 120

Total 120* 7 = 840

I know something is wrong with this approach but what exactly am I missing.

Re: Help with permutation n combination pblm [#permalink]

Show Tags

26 May 2012, 15:16

The committee has to be formed from 2 different groups of people (professors, graduates): So, 3 cases will be formed: 1P,2G 2P,1G 3P,0G 7C1*10C2 + 7C2*10C1 + 7C3*10C0

Re: Help with permutation n combination pblm [#permalink]

Show Tags

26 May 2012, 19:45

The missing part in this approach is that you cannot merge both the groups together as when you try to select out of 16 persons the next 2 people then you have included both the professors and the graduates.So if you try to select 2 people out of the 16 from the lot then you can again select professors also.

This question asks you to give the combinations of the committee wherein the committee could be differentiated on the basis of the number of the people selected from two groups (professors/graduates).

Re: A three-person committee must be chosen from a group of 7 [#permalink]

Show Tags

27 May 2012, 22:02

I agree that if I try to select 2 people out of the 16 from the lot then you can again select professors also. But thats what the requirement is i.e. One should be professor, that we have already selected, and for remaining two seats we don't have a specific condition i.e. whether they have to Professors or Graduates. Even your set 3P,0G points to the condition where no Grad is selected.
_________________

First say to yourself what you would be; and then do what you have to do.

Re: A three-person committee must be chosen from a group of 7 [#permalink]

Show Tags

27 May 2012, 23:36

5

This post received KUDOS

@anujkch, The answer to your question first:

When you do 7C1*16C2, you make a critical error. Consider the 7 professors to be A,B,C,D,E,F,G. Supposing you select A to be separate (i.e. part of the 7C1 selection) and the other two professors to be selected from B through G. You will then get a case A(BC). Now consider the case where you select B as part of the separate case, and choose the other two professors from A,C,D,E,F,G,H. Again you will get a case B(AC), which is the same as ABC in terms of selection. Therefore your method causes double counting at places and gives you an answer which is greater than the actual one.

@ankitbansal85, The error you make is different. In the PPP case, 7*6*5 is the number of ways you can arrange, and not just select three professors from 7 professors (i.e. 7*6*5 = 7P3). The number of ways to select 3 professors from 7 professors is 7C3. Similarly, in the PSS case, you must use 7*10C2, not 7*10*9, the latter is the number of ways to arrange 1 professor and 2 students in a row, not just select them. Correct this approach and you will get the right answer.

As for the right answer, it can be obtained in multiple ways, Method 1: 7C1 * 10C2 + 7C2 * 10C1 + 7C3 = 315 + 210 + 35 = 560

Method 2: Total number of ways to select at least one professor = Number of ways to select 3 people from 10 students and 7 professors - Number of ways to select 3 people from 10 student (i.e. without including any professor) = 17C3 - 10C3 = 680 - 120 = 560
_________________

Re: A three-person committee must be chosen from a group of 7 [#permalink]

Show Tags

28 May 2012, 00:42

@ankitbansal85,

Here is some theory behind it to help you understand better: Suppose you have three people A,B, and C. How many ways can you: 1) Arrange them in a row? 2) Select two from these three?

Ans: 1) The number of ways to arrange them in a row are ABC,BCA,CAB,ACB,BAC,and CBA for a total of 6 ways. 3! = 6, so the number of ways to arrange n people in a row is simply n! 2) Two can be selected from these three in just three ways: AB, BC, or CA. Remember that the selection AB is the same as the selection BA because in selections order does not matter. Therefore number of ways to select = 3C2 = 3 ways. Therefore the number of ways to select r objects from n different object is simply nCr.

Re: A three-person committee must be chosen from a group of 7 [#permalink]

Show Tags

24 Sep 2012, 07:48

Number of Professors - 7

Number of Students - 10

Committee size - 3

CONDITION - At least ONE professor per committee

With these conditions we can formulate the following scenarios :

Scenario I) 1 Professor and 2 Students Scenario II) 2 professors and 1 student Scenario III) 3 professors and ZERO students (this is the only tricky part of the question, WE HAVE to assume that the committee can consist of only professors since it is not explicitly mentioned in the question that their must be a "student representative" in the committee )

Solving I --> C(7,1) x C(10,2) = 7 x 45 = 315 Solving II --> C(7,2) x C (10,1) = 21 x 10 = 210 Solving III --> C(7,3) x C (10,0) = 35 x 1 = 35

Adding I , II and III we get 560 (B)
_________________

"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Re: A three-person committee must be chosen from a group of 7 [#permalink]

Show Tags

19 May 2013, 11:55

1

This post received KUDOS

1

This post was BOOKMARKED

The question stem states that at least 1 professor should be present. So all combinations of 3 people out of 17 people minus the combinations that no professors are present will give the answer:

All combinations: 17! / (3! 14!) = 680. No professors present: 10! / 3! 7! = 120.

Re: A three-person committee must be chosen from a group of 7 [#permalink]

Show Tags

24 Oct 2014, 07:04

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.
_________________

Re: A three-person committee must be chosen from a group of 7 [#permalink]

Show Tags

03 Oct 2016, 03:24

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.
_________________

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...