• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 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 PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote Five people, Ada, Ben, Cathy, Dan, and Eliza, are tagged by: Vincen This topic has 3 expert replies and 0 member replies Top Member Five people, Ada, Ben, Cathy, Dan, and Eliza, are Five people, Ada, Ben, Cathy, Dan, and Eliza, are lining up for a photo. What is the probability that none of the three girls will stand next to one another? (A) 0.1 (B) 0.2 (C) 0.3 (D) 0.4 (E) 0.5 The OA is A . I don't know what formula should I set. Can any expert give me some help? Please. GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello Vincen. Let's take a look at your question. The only option that none of the three girls will stand next to one another is that they stand in the first, third and fifth places. So, they have 3! options to stand. And the boys has 2! options. The total of possible options is 5!. So, the answer is $$\frac{3!\cdot2!}{5!}=\frac{1}{10}=0.1.$$ The correct answer is A . I hope this explanation may help you. I'm available if you'd like a follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. 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. GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 497 members Upvotes: 2867 GMAT Score: 800 Hi Vincen, We're given 3 girls and 2 boys and told to put them in a line. We're asked for the probability that none of the three girls will stand next to one another. This question can be approached in a number of different ways. Here's how you can use permutations and probability to get to the correct answer: With 5 people, there are 5! = 120 possible arrangements. Lining up the 5 people, there's just one option for the 3 girls to NOT stand next to one another: GBGBG = (3)(2)(2)(1)(1) = 12 options Thus, the probability of the 3 girls NOT standing next to one another is 12/120 = 1/10 = 10% = .1 Final Answer: A GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 Vincen wrote: Five people, Ada, Ben, Cathy, Dan, and Eliza, are lining up for a photo. What is the probability that none of the three girls will stand next to one another? (A) 0.1 (B) 0.2 (C) 0.3 (D) 0.4 (E) 0.5 For the 3 girls to be separated, they must occupy the first, third and fifth positions, as follows: G_G_G. P(girl occupies the first position) = 3/5. (Of the 5 children, 3 are girls.) P(girl occupies the third position) = 2/4. (Of the 4 remaining children, 2 are girls, since 1 of the 3 girls occupies the first position.) P(girl occupies the fifth position) = 1/3. (Of the 3 remaining children, only 1 is a girl, since 2 of the 3 girls occupy the first and third positions.) To combine these probabilities, we multiply: 3/5 * 2/4 * 1/3 = 1/10. The correct answer is A. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

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 Scott@TargetTestPrep

Target Test Prep

139 posts
2 Max@Math Revolution

Math Revolution

90 posts
3 Ian Stewart

GMATiX Teacher

53 posts
4 Brent@GMATPrepNow

GMAT Prep Now Teacher

51 posts
5 Jay@ManhattanReview

Manhattan Review

31 posts
See More Top Beat The GMAT Experts