• EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • 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
  • 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
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • 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
  • 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
  • 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
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist 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

There are 6 children at a family reunion, 3 boys and 3 girls

This topic has 3 expert replies and 1 member reply

There are 6 children at a family reunion, 3 boys and 3 girls

Post Sun Feb 18, 2018 1:14 pm
There are 6 children at a family reunion, 3 boys, and 3 girls. They will be lined up single-file for a photo, alternating genders. How many arrangements of the children are possible for this photo?

A. 54
B. 72
C. 18
D. 81
E. 36

The OA is B.

I'm confused by this PS question. Experts, any suggestion? I always have troubles with the combination questions.. Thanks in advance.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

ErikaPrepScholar Legendary Member
Joined
20 Jul 2017
Posted:
503 messages
Followed by:
9 members
Upvotes:
86
GMAT Score:
770
Post Mon Feb 19, 2018 5:30 am
We know that we *must* alternate boys and girls. This means we have two options for the order of boys and girls:

B--G--B--G--B--G
or
G--B--G--B--G--B

Within each of these two options, the boys can be arranged in any order and the girls can be arranged in any order. So we can think about this problem as:

2 order options * possible arrangements of 3 boys * possible arrangements of 3 girls

There are 3 boys and 3 girls. This means that the total number of arrangements for each is 3! - 3*2*1 = 6. So our equation is
2 order options * 6 arrangements of 3 boys * 6 arrangements of 3 girls
2 * 6 * 6 = 72

So there are 72 total arrangements of children available for the photo.

_________________


Erika John - Content Manager/Lead Instructor
https://gmat.prepscholar.com/gmat/s/

Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/

Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial

Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Mon Feb 19, 2018 2:16 pm
Hi LUANDATO,

We're told that 3 boys and 3 girls will be lined up single-file for a photo, alternating genders. We're asked for the number of arrangements of the children that are possible for this photo. This question is a fairly standard Permutation question with one small 'twist.'

Since the first child in line can be EITHER a boy or a girl, there are 6 options for that 1st spot. Once you put someone there though, the 2nd spot must be the OTHER gender, so...
there are 3 spots for the 2nd spot.

From there, the genders are boy-girl-boy-girl or girl-boy-girl-boy (depending who was in the 1st spot...
there are 2 spots for the 3rd spot.
there are 2 spots for the 4th spot.
there are 1 spots for the 5th spot.
there are 1 spots for the 6th spot.

Total arrangements = (6)(3)(2)(2)(1)(1) = 72

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag
Post Wed Feb 21, 2018 1:36 pm
LUANDATO wrote:
There are 6 children at a family reunion, 3 boys, and 3 girls. They will be lined up single-file for a photo, alternating genders. How many arrangements of the children are possible for this photo?

A. 54
B. 72
C. 18
D. 81
E. 36
We can have the following arrangements:

BGBGBG or GBGBGB

Since the number of people in the arrangement is the same, the number of arrangements for each is the same. Let’s tackle the first arrangement.

For the first position, we have 3 possible boys to choose from. For the second position, we have 3 girls to choose from. For the third position, we have 2 boys, and for the fourth position we have 2 girls, and for the fifth, there is 1 boy, and for the sixth, there is 1 girl. Thus:
3 x 3 x 2 x 2 x 1 x 1 = 36 ways

So the total number of ways is 36 + 36 = 72 ways.

Answer: B

_________________
Jeffrey Miller Head of GMAT Instruction

  • +1 Upvote Post
  • Quote
  • Flag
Post Fri Mar 09, 2018 12:31 pm
Firstly, let us arrange the boys in a way that there is a gap that will be filled by a girl in between each boy.
There are 3 boys to arrange in 3 positions. Therefore the number of permutation possible= $$3P_2$$ = 6ways
Next, we fill up the remaining 3 gaps with 3 girls .
Number of possible permutation = $$3P_2$$ = 6ways
We have permuted the possibilities in this way B-G-B-G-B-G
But we can also have the arrangement in this way: G-B-G-B-G-B
This means that for every arrangement obtained earlier, there are 2 possible permutations.
Therefore the total number of arrangement possible = 2 * [6*6] =72 possible arrangements

we can confidently say option B is correct

  • +1 Upvote Post
  • Quote
  • Flag

Top First Responders*

1 GMATGuruNY 109 first replies
2 Brent@GMATPrepNow 43 first replies
3 Rich.C@EMPOWERgma... 35 first replies
4 Jay@ManhattanReview 31 first replies
5 Scott@TargetTestPrep 11 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 GMATGuruNY

The Princeton Review Teacher

158 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

140 posts
3 image description Scott@TargetTestPrep

Target Test Prep

104 posts
4 image description Jeff@TargetTestPrep

Target Test Prep

94 posts
5 image description Max@Math Revolution

Math Revolution

88 posts
See More Top Beat The GMAT Experts