NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 19:24 It is currently 25 Apr 2024, 19:24
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

How many different ways can 2 students be seated in a row of

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
ksharma12
Manager
Manager
Joined: 03 Feb 2010
Posts: 51
Own Kudos [?]: 565 [21]
Given Kudos: 4
Send PM
How many different ways can 2 students be seated in a row of [#permalink] New post   17 Feb 2010, 11:27
2
Kudos
19
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

60% (01:10) correct 40% (01:09) wrong based on 490 sessions
Hide Show timer Statistics
How many different ways can 2 students be seated in a row of 4 desks, so that there is always at least one empty desk between the students?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
honeyrai
Intern
Intern
Joined: 01 Feb 2010
Posts: 22
Own Kudos [?]: 51 [8]
Given Kudos: 12
Send PM
Re: How many different ways can 2 students be seated in a row of [#permalink] New post   21 Feb 2010, 00:55
5
Kudos
3
Bookmarks
ksharma12 wrote:
But that yields the same answer as 4C2? How do you solve use combinations or perm?

That comb above does not take into account the empty seat.

Here order is important, therefore, we'll use Perm.

All the possible ways in which 2 stud can be seated on 4 seats = 4P2.
Suppose, two students are always seated together. Then we'll treat them as 1 stud & the seats left to be filled are 3. Therefore no. of ways in which 2 stud are always seated together = 3P2.

Now, the no. of ways in which 2 students have a gap in between = total no. of ways - no. of ways in which students are seated together = 4P2-3P2 = 12-6 = 6
General Discussion
User avatar
LevFin7S
Intern
Intern
Joined: 14 Nov 2008
Posts: 22
Own Kudos [?]: 91 [2]
Given Kudos: 0
 Q48  V40
Send PM
Re: How many different ways can 2 students be seated in a row of [#permalink] New post   17 Feb 2010, 11:34
2
Kudos
3 ways to seat the students:
with two empty seats between
1 empty w/ one student on the left most
1 empty....right most

two students can be interchanged

3x2=6
User avatar
ksharma12
Manager
Manager
Joined: 03 Feb 2010
Posts: 51
Own Kudos [?]: 565 [0]
Given Kudos: 4
Send PM
Re: How many different ways can 2 students be seated in a row of [#permalink] New post   17 Feb 2010, 11:47
But that yields the same answer as 4C2? How do you solve use combinations or perm?

That comb above does not take into account the empty seat.
User avatar
gurpreetsingh
SVP
SVP
Joined: 12 Oct 2009
Status:<strong>Nothing comes easy: neither do I want.</strong>
Posts: 2279
Own Kudos [?]: 3594 [0]
Given Kudos: 235
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Send PM
Reviews Badge
Re: How many different ways can 2 students be seated in a row of [#permalink] New post   17 Feb 2010, 12:04
Take two cases.

case 1... 2 spaces in between that means C1 _ _ C2 or C2_ _ C1

case 2.... 1 space in between.
now consider c1_c2 as one element
Number of ways of arranging these in 4 seats = \(2p2*2!\) = 4

2p2 because we have considered c1_c2 as one element , 2! is rearrangement between c1 and c2

total = 6..whats OA?
User avatar
bangalorian2000
Manager
Manager
Joined: 01 Feb 2010
Posts: 90
Own Kudos [?]: 136 [0]
Given Kudos: 2
Send PM
Re: How many different ways can 2 students be seated in a row of [#permalink] New post   24 Feb 2010, 01:18
ksharma12 wrote:
How many different ways can 2 students be seated
in a row of 4 desks, so that there is always at
least one empty desk between the students?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
Easy Question I know. Explanation please?


Possible patterns = 1x2x, 1xx2, x1x2, 2x1x, x2x1, 2xx1 = 6 hence D

Whats the OA
User avatar
MyRedemption
Intern
Intern
Joined: 13 Aug 2013
Posts: 10
Own Kudos [?]: 10 [3]
Given Kudos: 1
Send PM
Re: How many different ways can 2 students be seated in a row of [#permalink] New post   13 Jul 2014, 01:31
1
Kudos
2
Bookmarks
Total cases : 12 ( student one has 4 options and student two has three options, 4x3=12)
Non-favourable cases : 6 (when two students sit together. students in desk 1 and desk 2 , in desk 2 and desk 3, in desk 3 and desk 4) for each of these cases there are two possibilities because the positions can be interchanged. hence 2x3=6.

SO favourable cases : 12-6=6.
User avatar
B
TooLong150
Manager
Manager
Joined: 10 Mar 2013
Posts: 137
Own Kudos [?]: 494 [0]
Given Kudos: 2412
GMAT 1: 620 Q44 V31
GMAT 2: 610 Q47 V28
GMAT 3: 700 Q49 V36
GMAT 4: 690 Q48 V35
GMAT 5: 750 Q49 V42
GMAT 6: 730 Q50 V39
GPA: 3
Send PM
Reviews Badge
How many different ways can 2 students be seated in a row of [#permalink] New post   26 Nov 2015, 10:49
It is important to see that the empty desks are not distinct (I missed this the first time, because I considered them to be)
We have "4" students (2 normal students {\(A\),\(B\)} and 2 students {\(E_1\),\(E_2\)} that we can consider empty desks) and 4 places.
Total = \(\frac{4!}{2!}\) since \(AE_1E_2B=AE_2E_1B\)
Cases in which the two students are together {{\(A\),\(B\)}, \(E_1\), \(E_2\)} = 3!*2!/2! since \(ABE_1E_2\) = \(ABE_2E_1\)
Total - together = 12 - 6 = 6
User avatar
L
EMPOWERgmatRichC
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21846
Own Kudos [?]: 11666 [1]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: How many different ways can 2 students be seated in a row of [#permalink] New post   26 Nov 2015, 16:44
1
Bookmarks
Expert Reply
Hi All,

Since the answers to this question are all small, and the question has a strong 'visual' component to it, we can 'brute force' the answer by drawing some pictures.

If we call the two students 'X' and 'Y', we have the following possibilities:

X _ Y _
Y _ X _

X _ _ Y
Y _ _ X

_ X _ Y
_ Y _ X

Total options: 6

Final Answer:
Show Spoiler
D


GMAT assassins aren't born, they're made,
Rich
User avatar
S
armaankumar
Manager
Manager
Joined: 10 Jun 2020
Posts: 103
Own Kudos [?]: 57 [0]
Given Kudos: 104
Location: India
Schools: ESSEC ESCP Europe (A) HEC MiM "25 (D)
GMAT 1: 610 Q41 V33 (Online)
GMAT 2: 650 Q47 V33 (Online)
GPA: 3.4
Send PM
Re: How many different ways can 2 students be seated in a row of [#permalink] New post   06 Aug 2021, 22:57
Students: A, B
Desks: _ _ _ _
Case 1: A _ B _ (A&B can switch places) : 2 Ways
Case 2: _ A _ B ( A&B can switch places) : 2 Ways
Case 3: A _ _ B (A &b B can switch places): 2 Ways

Total Ways: 2 + 2 + 2 = 6
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32680
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: How many different ways can 2 students be seated in a row of [#permalink] New post   08 May 2023, 08:39
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.
GMAT Club Bot
gmatclubot
Re: How many different ways can 2 students be seated in a row of [#permalink]
08 May 2023, 08:39
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions