• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

How many different ways are there to arrange . . .

This topic has 1 expert reply and 1 member reply

How many different ways are there to arrange . . .

Post
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

The OA is B.

Can any expert give me a detailed explanation of how can I solve this PS question? Thanks.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Top Reply
Post
Hello M7MBA.

We have to arrange 3 adults and 4 children in 7 seats in the following form: A C A C C C A.

For the first place, we have 3 options.
For the second place, we have 4 options.
For the third place, we have 2 options.
For the fourth place, we have 3 options.
For the fifth place, we have 2 options.
For the sixth place, we have 1 option.
For the seventh place, we have 1 option.

So, the total of options to arrange the 7 people is equal to 3*4*2*3*2*1*1 = 144.

So, the correct answer is B.

I hope this explanation may help you.

Feel free to ask me again if you have a doubt.

Regards.

_________________
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

  • +1 Upvote Post
  • Quote
  • Flag
Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.
Master | Next Rank: 500 Posts Default Avatar
Joined
29 Nov 2017
Posted:
100 messages
Upvotes:
14
Post
M7MBA 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

The OA is B.

Can any expert give me a detailed explanation of how can I solve this PS question? Thanks.
three adults can be placed in three seats in 3! ways = 3*2*!=6
four children can be placed in four seats in 4! ways =4*3*2*1=24
Hence total number of ways = 6*24= 144
So B is the correct option.

  • +1 Upvote Post
  • Quote
  • Flag
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep

Top First Responders*

1 Ian Stewart 44 first replies
2 Brent@GMATPrepNow 34 first replies
3 Scott@TargetTestPrep 32 first replies
4 Jay@ManhattanReview 31 first replies
5 GMATGuruNY 18 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

139 posts
2 image description Max@Math Revolution

Math Revolution

90 posts
3 image description Ian Stewart

GMATiX Teacher

53 posts
4 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

51 posts
5 image description Jay@ManhattanReview

Manhattan Review

31 posts
See More Top Beat The GMAT Experts