• 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 ## in how many ways 5 different chocolates be distributed . . . tagged by: VJesus12 ##### This topic has 2 expert replies and 0 member replies ### Top Member ## in how many ways 5 different chocolates be distributed . . . in how many ways 5 different chocolates be distributed to 4 children such that any child can get any number of chocolates? 1) 20 2) 24 3) 120 4) 625 5) 1024 The OA is the option E. How can I get the correct answer here? Can any expert help me? I don't know how to solve this PS question. ### GMAT/MBA Expert Legendary Member Joined 20 Jul 2017 Posted: 503 messages Followed by: 11 members Upvotes: 86 GMAT Score: 770 We must distribute 5 chocolates among 4 children. We know that any child can get any number of chocolates. This means that 3 children could get 1 chocolate and 1 child could get 2 chocolates; or 1 child could get all 5 chocolates and 3 children could get 0 chocolates; or 1 children could get 3 chocolates, 2 children could get 1 chocolate, and 1 child could get 0 chocolates; etc. etc. This is pretty complex, but we can actually think about it in a pretty simple way. Since which child gets which chocolate next doesn't depend at all on which children already have chocolates, we can think of the distribution of each piece of chocolate independently. The first chocolate can go to any of the 4 children. That's 4 options. For each of those options, the second chocolate can go to any of the 4 children. That's another 4 options. This means that there are 4*4=16 options for how the first two chocolates can be given away. For each of those options, the third chocolate can go to any of the 4 children. That's another 4 options. This means that there are 4*4*4=64 options for how the first three chocolates can be given away. For each of those options, the fourth chocolate can go to any of the 4 children. That's another 4 options. This means that there are 4*4*4*4=256 options for how the first four chocolates can be given away. For each of those options, the fifth chocolate can go to any of the 4 children. That's another 4 options. This means that there are 4*4*4*4*4=1024 options for how all four chocolates can be given away. This gives us the correct answer, E. _________________ 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 ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello Vjesus12. Let's take a look at your question. Let the 5 cholcolates be : C1 , C2 , C3 , C4 and C5. And there be 4 Students : S1 , S2, S3 and S4. Now, The first Chocolate can be given in 4 ways (Either to S1 or S2 or S3 or S4). The Second Chocolate can be given in 4 ways (Either to S1 or S2 or S3 or S4). The Third Chocolate can be given in 4 ways (Either to S1 or S2 or S3 or S4). The Fourth Chocolate can be given in 4 ways (Either to S1 or S2 or S3 or S4). The Fifth Chocolate can be given in 4 ways (Either to S1 or S2 or S3 or S4). So, we have $$4\cdot4\cdot4\cdot4\cdot4=4^5=1,024\ possible\ ways.$$ This is why the correct answer is the option E . I hope this answer can help you. I'm available if you'd like a follow-up. Regards. _________________ 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. • Free Veritas GMAT Class Experience Lesson 1 Live Free 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

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

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

• 5 Day FREE Trial
Study Smarter, Not Harder

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

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

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

Available with Beat the GMAT members only code

### Top First Responders*

1 Brent@GMATPrepNow 40 first replies
2 Ian Stewart 40 first replies
3 Scott@TargetTestPrep 39 first replies
4 Jay@ManhattanReview 28 first replies
5 GMATGuruNY 25 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

159 posts
2 Max@Math Revolution

Math Revolution

90 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

58 posts
4 Ian Stewart

GMATiX Teacher

49 posts
5 GMATGuruNY

The Princeton Review Teacher

38 posts
See More Top Beat The GMAT Experts