Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
itsworththepain
GMAT 1: 720 Q49 V38
Posts: 12
Updated on: 27 Jun 2014, 01:47
Originally posted by itsworththepain on 26 Jun 2014, 23:53.
Last edited by Bunuel on 27 Jun 2014, 01:47, edited 2 times in total.
Last edited by Bunuel on 27 Jun 2014, 01:47, edited 2 times in total.
Edited the question and added the OA.
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
55% (01:05) correct
45%
(01:34)
wrong
based on 959
sessions
History
Date
Time
Result
Not Attempted Yet
In how many ways can 5 different fruits be distributed among four children? (Some children may get more than one fruit and some may get no fruits.)
(A) 4^5
(B) 5^4
(C) 5!
(D) 4!
(E) 4!*5!
(A) 4^5
(B) 5^4
(C) 5!
(D) 4!
(E) 4!*5!
Correct Answer is 1024 and I understand the reasoning behind that.
But the approach I followed was:
Say we keep the 5th fruit aside and distribute the other 4 fruits among the 4 children
No of ways to distribute 4 fruits among 4 children = 4!
Now for each of these 4! Combinations, 5th fruit can be distributed to any of the 4 children
i.e. 4 new combinations for each of the 4! combinations
No of ways to distribute 5th fruit = 4*4!
5th fruit can be selected in 5 different ways
Total combinations are 5*4*4! = 480
What’s wrong here? What is it that I am missing here? What are the other 1024-480 combinations that I am missing?
But the approach I followed was:
Say we keep the 5th fruit aside and distribute the other 4 fruits among the 4 children
No of ways to distribute 4 fruits among 4 children = 4!
Now for each of these 4! Combinations, 5th fruit can be distributed to any of the 4 children
i.e. 4 new combinations for each of the 4! combinations
No of ways to distribute 5th fruit = 4*4!
5th fruit can be selected in 5 different ways
Total combinations are 5*4*4! = 480
What’s wrong here? What is it that I am missing here? What are the other 1024-480 combinations that I am missing?
27 Jun 2014, 00:08
Kudos
Bookmarks
sagarsameer
I believe you picked up this question from my blog post so you know how to correctly solve it. So I will focus on only pointing out the error you committed. To start off, how do you get "No of ways to distribute 4 fruits among 4 children = 4! "? You are not given that each child gets only one fruit. If each child were to receive only one fruit, then you could have said that the first fruit can be given away in 4 ways, 2nd fruit in 3 ways and so on to get 4*3*2*1.
Some children may get none so others may get 2 or 3 or 4. Each fruit can be given out in 4 ways so 4*4*4*4*4 = 1024
Mugdho
There are 5 diff fruits to be distributed among 4 children.
First person does not choose a fruit in 5 ways. That would have been true if each child were to pick exactly 1 fruit. But here a child may not get any fruit and another may get 2 or more.
The only thing we know is that all 5 fruits are distributed. So each fruit gets an owner. Fruit 1 can be given away in 4 ways (to any one of the 4 children). Fruit 2 can be again given away in 4 ways to any 1 of the 4 children and so on.
There is no constraint on how many fruits each child may get.
That is why we get 4*4*4*4*4.
All these cases with small variations with distinct and identical objects (total 16 cases) are covered in our Combinatorics module in detail here. You can check it out using the 3 day trial.
https://anaprep.com
