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

It is currently 20 Oct 2019, 05:08

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.

Close

Request Expert Reply

Confirm Cancel

In how many ways can you seat 7 people on a bench if one of

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
User avatar
Status: Learning
Joined: 07 Aug 2011
Posts: 36
Location: India
Schools: WBUT - Class of 2011
GMAT Date: 01-06-2014
GPA: 2.6
WE: Research (Education)
In how many ways can you seat 7 people on a bench if one of  [#permalink]

Show Tags

New post Updated on: 01 Nov 2013, 01:02
1
4
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

76% (01:52) correct 24% (01:58) wrong based on 242 sessions

HideShow timer Statistics

In how many ways can you seat 7 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?

A) 720
B) 1720
C) 2880
D) 5040
E) 10080

_________________
If you like my post give me kudos.

Arindam Sur
Researcher, Academian

Originally posted by arindamsur on 31 Oct 2013, 23:16.
Last edited by arindamsur on 01 Nov 2013, 01:02, edited 2 times in total.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58434
Re: In how many ways can you seat 7 people on a bench if one of  [#permalink]

Show Tags

New post 01 Nov 2013, 00:43
3
1
arindamsur wrote:
In how many ways can you seat 7 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?

A) 720
B) 1720
C) 2880
D) 5040
E) 10080


Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 4 chairs to sit. The remaining 6 people can sit in 6! ways. Thus the # of arrangements is 4*6! = 2,880.

Answer: C.
_________________
Intern
Intern
avatar
Joined: 17 Sep 2013
Posts: 24
Location: United States
Concentration: Economics, Statistics
Schools: CBS '18 (M)
GMAT 1: 770 Q51 V45
GPA: 3.36
WE: Analyst (Health Care)
GMAT ToolKit User Reviews Badge
Re: In how many ways can you seat 7 people on a bench if one of  [#permalink]

Show Tags

New post 01 Nov 2013, 09:48
1
There are 7! total ways to sit everyone.

There are 3 seats that he can't sit in (the two ends and the middle). For each seat of the 3 seats he can't sit in, there are 6! arrangements of people in the other seats. So the total number of arrangements where he isn't sitting in any of those three seats is:

7! - 6!(3) =
6!(7 - 3) =
6!(4) =
2880
Intern
Intern
User avatar
Status: Bring it on.....!
Joined: 11 Jul 2013
Posts: 24
Location: India
Concentration: Technology
GMAT 1: 660 Q49 V31
Re: In how many ways can you seat 7 people on a bench if one of  [#permalink]

Show Tags

New post 02 Nov 2013, 01:42
1
total no of ways in which all 7 can be seated = 7! ways

now,
if rohit sits at first seat then remaining 6 can be seated in 6! ways
if rohit sits at middle seat then remaining 6 can be seated in 6! ways
if rohit sits at last seat then remaining 6 can be seated in 6! ways

no. of ways in which rohit doesnt sits in middle or at either ends = 7! - (6! + 6! + 6!) = 7! - 6!*3 = 6!(7-3)=6!*4=2880

Hope this helps.
_________________
Live as if your were to die tomorrow. Learn as if you were to live forever - Gandhi
GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 5022
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member
Re: In how many ways can you seat 7 people on a bench if one of  [#permalink]

Show Tags

New post 27 Jan 2019, 01:36
total seating arragements = 7!
for Rohit who supposedly sits on first chair ; then 6! ways for others
middle seat : again 6! and last seat 6!

so total ways in which all of them can sit
7!-3*6!
6! ( 7-3)
6!*4
= > 2880
IMO C

arindamsur wrote:
In how many ways can you seat 7 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?

A) 720
B) 1720
C) 2880
D) 5040
E) 10080
GMAT Club Bot
Re: In how many ways can you seat 7 people on a bench if one of   [#permalink] 27 Jan 2019, 01:36
Display posts from previous: Sort by

In how many ways can you seat 7 people on a bench if one of

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne