GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 04:44

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

From the following list of five question stems, how many are permutati

Author Message
TAGS:

Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 822
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
From the following list of five question stems, how many are permutati  [#permalink]

Show Tags

20 Sep 2015, 06:03
2
From the following list of five question stems, how many are permutations questions and how many are combinations questions?

I. How many ways can ten students arrange themselves in a row of ten seats?
II. How many groups of students can attend a conference if there are ten students and four passes to attend the conference?
III. How many subcommittees of four are possible from a committee of 12 people?
IV. How many ways can Karl arrange his twelve books on a shelf?
V. How many seating arrangements are possible for six couples sitting around a circular table?

A. 1 permutation, 4 combination
B. 2 permutation, 3 combination
C. 3 permutation, 2 combination
D. 4 permutation, 1 combination
E. All five are permutation questions

Could somone please A.) comment each question on the list with the answer to the question and B.) explain how one easily recognises that the question is a permutation or combination problem.
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.
CEO
Joined: 20 Mar 2014
Posts: 2603
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: From the following list of five question stems, how many are permutati  [#permalink]

Show Tags

20 Sep 2015, 06:43
1
reto wrote:
From the following list of five question stems, how many are permutations questions and how many are combinations questions?

I. How many ways can ten students arrange themselves in a row of ten seats?
II. How many groups of students can attend a conference if there are ten students and four passes to attend the conference?
III. How many subcommittees of four are possible from a committee of 12 people?
IV. How many ways can Karl arrange his twelve books on a shelf?
V. How many seating arrangements are possible for six couples sitting around a circular table?

A. 1 permutation, 4 combination
B. 2 permutation, 3 combination
C. 3 permutation, 2 combination
D. 4 permutation, 1 combination
E. All five are permutation questions

Could somone please A.) comment each question on the list with the answer to the question and B.) explain how one easily recognises that the question is a permutation or combination problem.

I. How many ways can ten students arrange themselves in a row of ten seats? = n arragements of n objects = n! = P. The order matters. Take the case of a 3 books in 3 slots. ABC is different than BAC or CBA. Thus the order is important.

II. How many groups of students can attend a conference if there are ten students and four passes to attend the conference? = C. The order is not important. If I have to select ABCD for the 4 passes, then it does not matter whether I choose these 4 people as BACD or ADCB or BCDA etc.

III. How many subcommittees of four are possible from a committee of 12 people? = C, I dont care if the chosen people are a,b,c,d or a,c,d,b or b,c,d,a. The committee of 4 still remains the same.

IV. How many ways can Karl arrange his twelve books on a shelf? = P, the order matters similar to case (i).

V. How many seating arrangements are possible for six couples sitting around a circular table? = CIRCULAR ARRANGEMENT, depending on whether the order (clockwise vs anticlockwise) is important, you will get 2 different answers. Can not be categorized as either permutation or combination.

Basic principles are: $$nCr = \frac {n!}{r!*(n-r)!}$$ and . Thus you see nPr = nCr * r! ----> Permutations specify order of selection while combinations do not cater to the order. In other words, if a selection is highly ORDERED, it is permutation, while if the order is NOT important, it will be combination.

Example, lets say I talk about a lock that has the code of 123. Then ONLY 123 will work. 321 or 132 or 231 will NOT work. Thus the order matters. This case is of permutation.

But if I tell you that I need 3 fruit out of a mixture of 5, then I do not care whether you pick a,b,c or you pick b,a,c. You will still end up getting a combination of 3 same fruits. In this case, you have combinations.

Read here for more : math-combinatorics-87345.html

Veritas prep's book on combinatorics is also a good study material with good collection of problems.

Additionally, most of GMAT combinatorics problems can be solved via counting principle (a simpler way of calculating possible arrangements without the fanciness of 'factorials' or particular formulae of permutations or combinations!).

For combinatorics questions :

PS : search.php?search_id=tag&tag_id=52
DS: search.php?search_id=tag&tag_id=31

Hope this helps.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9699
Location: Pune, India
Re: From the following list of five question stems, how many are permutati  [#permalink]

Show Tags

21 Sep 2015, 00:05
1
reto wrote:
From the following list of five question stems, how many are permutations questions and how many are combinations questions?

I. How many ways can ten students arrange themselves in a row of ten seats?
II. How many groups of students can attend a conference if there are ten students and four passes to attend the conference?
III. How many subcommittees of four are possible from a committee of 12 people?
IV. How many ways can Karl arrange his twelve books on a shelf?
V. How many seating arrangements are possible for six couples sitting around a circular table?

A. 1 permutation, 4 combination
B. 2 permutation, 3 combination
C. 3 permutation, 2 combination
D. 4 permutation, 1 combination
E. All five are permutation questions

Could somone please A.) comment each question on the list with the answer to the question and B.) explain how one easily recognises that the question is a permutation or combination problem.

Here are the keywords:
Combination - Selection
Permutation - Arrangement

I. How many ways can ten students arrange themselves in a row of ten seats?
Arrange themselves - Permutation

II. How many groups of students can attend a conference if there are ten students and four passes to attend the conference?
Out of 10, select 4 for 4 passes - Combination

III. How many subcommittees of four are possible from a committee of 12 people?
Out of 12, select 4 - Combination

IV. How many ways can Karl arrange his twelve books on a shelf?
Arrange 12 - Permutation

V. How many seating arrangements are possible for six couples sitting around a circular table?
Arrange six couples - Permutation

Often, questions have both permutation and combination. e.g.

How many different results are possible for a race of 10 students if the results give ranks of first, second and third?

Out of 10 students, you need to select 3 - Combination
and then arrange the three into first, second third positions - Permutation
_________________
Karishma
Veritas Prep GMAT Instructor

Non-Human User
Joined: 09 Sep 2013
Posts: 13095
Re: From the following list of five question stems, how many are permutati  [#permalink]

Show Tags

29 Jan 2018, 00:49
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: From the following list of five question stems, how many are permutati   [#permalink] 29 Jan 2018, 00:49
Display posts from previous: Sort by