• 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 ## Triplets Adam, Bruce, and Charlie enter a triathlon. If ther ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Triplets Adam, Bruce, and Charlie enter a triathlon. If ther ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Triplets Adam, Bruce, and Charlie enter a triathlon. If there are 9 competitors in the triathlon, and medals are awarded for first, second, and third place, what is the probability that at least two of the triplets will win a medal? A. 3/14 B. 19/84 C. 11/42 D. 15/28 E. 3/4 OA B Source: Manhattan Prep ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2012 messages Followed by: 14 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: Triplets Adam, Bruce, and Charlie enter a triathlon. If there are 9 competitors in the triathlon, and medals are awarded for first, second, and third place, what is the probability that at least two of the triplets will win a medal? A. 3/14 B. 19/84 C. 11/42 D. 15/28 E. 3/4 The total number of ways to select 3 people from 9 is 9C3 = (9 x 8 x 7)/(3 x 2) = 3 x 4 x 7 = 84. The number of ways 2 of the triplets are among the 3 awarded is 3C2 x 6C1 = 3 x 6 = 18. The number of ways all 3 triplets are the 3 awarded is 3C3 x 6C0 = 1 x 1 = 1. Therefore, the probability is (18 + 1)/84 = 19/84. Answer: B _________________ Scott Woodbury-Stewart Founder and CEO ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1282 messages Followed by: 29 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: Triplets Adam, Bruce, and Charlie enter a triathlon. If there are 9 competitors in the triathlon, and medals are awarded for first, second, and third place, what is the probability that at least two of the triplets will win a medal? A. 3/14 B. 19/84 C. 11/42 D. 15/28 E. 3/4 Source: Manhattan Prep $$\left\{ \matrix{ \,A\,,B\,,\,{\kern 1pt} C\,\,\,\,\, \to \,\,\,3\,\,{\rm{competitors}} \hfill \cr \,{\rm{D,}}\,\, \ldots \,\,{\rm{,}}\,I\,\,\, \to \,\,\,{\rm{other}}\,\,6\,\,{\rm{competitors}}\, \hfill \cr} \right.$$ $$\left( {\rm{i}} \right)\,\,A,B,C\,\,{\rm{win}}\,\,{\rm{the}}\,\,3\,\,{\rm{medals}}$$ $$\left( {{\rm{ii}}} \right)\,\,A,B,C\,\,{\rm{win}}\,\,{\rm{exactly}}\,\,2\,\,{\rm{of}}\,\,{\rm{the}}\,\,3\,\,{\rm{medals}}$$ $$? = P\left( {{\rm{i}}\,\,{\rm{or}}\,\,{\rm{ii}}} \right) = P\left( {\rm{i}} \right) + P\left( {{\rm{ii}}} \right)\,\,\,\,\,\,\,\,\left[ {\,{\rm{i}}\,\,{\rm{and}}\,\,{\rm{ii}}\,\,{\rm{are}}\,\,{\rm{mutually}}\,\,{\rm{exclusive}}\,} \right]$$ $$\left( {\rm{i}} \right)\,\,\,\left\{ \matrix{ \,{\rm{favorable}} = \,\,3! \hfill \cr \,{\rm{total}}\,\, = \,\,9 \cdot 8 \cdot 7\,\,{\rm{equiprobables}}\,\,\, \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,P\left( {\rm{i}} \right) = {1 \over {84}}$$ $$\left( {{\rm{ii}}} \right)\,\,\,\left\{ \matrix{ \,{\rm{favorable}} = \,\,\underbrace {C\left( {3,2} \right)}_{{\rm{say}}\,\,A,B}\,\,\, \cdot \,\,\underbrace {C\left( {3,2} \right)}_{{\rm{say}}\,\,\,1{\rm{st}}\,\,,\,\,2{\rm{nd}}}\,\,\, \cdot \,\,\underbrace {2!}_{{\rm{say}}\,\,\,A\,\,1{\rm{st}}\,\,,\,B\,\,2{\rm{nd}}}\,\,\, \cdot \,\,\,\underbrace {C\left( {6,1} \right)}_{{\rm{say}}\,\,D\,\,\left( {3{\rm{rd}}} \right)}\, \hfill \cr \,{\rm{total}}\,\, = \,\,9 \cdot 8 \cdot 7\,\,{\rm{equiprobables}}\,\,\, \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,P\left( {{\rm{ii}}} \right) = {3 \over {14}}$$ $$? = {1 \over {84}} + {{3 \cdot 6} \over {14 \cdot 6}} = {{19} \over {84}}$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15103 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorDC wrote: Triplets Adam, Bruce, and Charlie enter a triathlon. If there are 9 competitors in the triathlon, and medals are awarded for first, second, and third place, what is the probability that at least two of the triplets will win a medal? A. 3/14 B. 19/84 C. 11/42 D. 15/28 E. 3/4 One approach: P(good outcome) = 1 - P(bad outcome). Bad outcome #1: Exactly 1 triplet wins. P(triplet wins 1st place) = 3/9. (Of the 9 competitors, 3 are triplets) P(non-triplet wins 2nd place) = 6/8. (Of the 8 remaining competitors, 6 are non-triplets) P(non-triplet wins 3rd place) = 5/7. (Of the 7 remaining competitors, 5 are non-triplets). Since we want all of these events to happen together, we multiply: 3/9 * 6/8 * 5/7 = 5/28. Since the triplet who wins could be in 1st, 2nd or 3rd place, we multiply by 3: 3 * 5/28 = 15/28. Bad outcome #2: None of the triplets wins. P(non-triplet wins 1st place) = 6/9. (Of the 9 competitors, 6 are non-triplets) P(non-triplet wins 2nd place) = 5/8. (Of the 8 remaining competitors, 5 are non-triplets) P(non-triplet wins 3rd place) = 4/7. (Of the 7 remaining competitors, 4 are non-triplets). Since we want all of these events to happen together, we multiply: 6/9 * 5/8 * 4/7 = 5/21. P(at least 1 triplet wins) = 1 - 15/28 - 5/21 = 1 - 45/84 - 20/84 = 19/84. The correct answer is B. _________________ 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. • 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

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• 1 Hour Free
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

• Magoosh
Study with Magoosh GMAT prep

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

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

### Top First Responders*

1 fskilnik@GMATH 55 first replies
2 GMATGuruNY 52 first replies
3 Brent@GMATPrepNow 51 first replies
4 Jay@ManhattanReview 39 first replies
5 Rich.C@EMPOWERgma... 23 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

198 posts
2 fskilnik@GMATH

GMATH Teacher

154 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

97 posts
4 Max@Math Revolution

Math Revolution

89 posts
5 GMATGuruNY

The Princeton Review Teacher

76 posts
See More Top Beat The GMAT Experts