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

It is currently 13 Oct 2019, 20:29

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

How many different ways are there to arrange a group of 3 adults and 4

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58335
How many different ways are there to arrange a group of 3 adults and 4  [#permalink]

Show Tags

New post 13 Dec 2016, 06:49
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

89% (01:23) correct 11% (01:25) wrong based on 143 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 359
GPA: 3.98
Re: How many different ways are there to arrange a group of 3 adults and 4  [#permalink]

Show Tags

New post 13 Dec 2016, 07:56
There are 3 adults that should be seated on three particular seats and 4 children on the rest four. Adults and children cannot switch places with each other, only among themselves

Hence: \(3!*4! = 6*24 = 144\)

Answer B
Intern
Intern
avatar
B
Joined: 12 Feb 2017
Posts: 4
How many different ways are there to arrange a group of 3 adults and 4  [#permalink]

Show Tags

New post 10 Dec 2017, 07:04
the adults have to be in 1 3 and 7th place , therefore : A*c*A*c*c*c*A
so it will be 3 x C x 2 x C x C x C x 1

now the children taking remaining places will be
3 x 4 x 2 x 3 x 2 x 1 x 1 = 144
Intern
Intern
avatar
Joined: 10 Dec 2017
Posts: 3
Re: How many different ways are there to arrange a group of 3 adults and 4  [#permalink]

Show Tags

New post 10 Dec 2017, 07:58
Bunuel wrote:
How many different ways are there to arrange a group of 3 adults and 4 children in 7 seats if adults must have the first, third, and 7 seats?

A. 12
B. 144
C. 288
D. 1,400
E. 5,040



Answer: 3 adults can be seated in 1st, 3rd and 7 th position in 3! ways. The remaining 4 positions are occupied by the remaining 4 people in 4! ways. Hence the total number of seating arrangements are 3!*4! = 144 ways.

Sneha Tatavarthy
Math Facililator
International Baccalaureate
_________________
Regards,
Sneha Tatavarthy
Math Facilitator
International Baccalaureate
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15228
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: How many different ways are there to arrange a group of 3 adults and 4  [#permalink]

Show Tags

New post 04 Jan 2018, 15:37
Hi All,

We're asked to arrange a group of 3 adults and 4 children in 7 seats with adults in the first, third, and seventh seats. We're asked for the number of arrangements possible. This question is a variation on a standard Permutation question. To solve it, we have to go from space to space and keep track of the 'options' available for each (noting that once we place a person, there is one fewer person available for the next equivalent spot).

For the 1st spot, there are 3 options
For the 2nd spot, there are 4 options
For the 3rd spot, there are 2 options
For the 4th spot, there are 3 options
For the 5th spot, there are 2 options
For the 6th spot, there are 1 options
For the 7th spot, there are 1 options

Total arrangements = (3)(4)(2)(3)(2)(1)(1) = 144 possible arrangments

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
GMAT Club Bot
Re: How many different ways are there to arrange a group of 3 adults and 4   [#permalink] 04 Jan 2018, 15:37
Display posts from previous: Sort by

How many different ways are there to arrange a group of 3 adults and 4

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





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