GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 28 Mar 2020, 22:08

### 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In how many ways can 6 chocolates be distributed among 3 children? A c

Author Message
TAGS:

### Hide Tags

CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3396
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

### Show Tags

16 May 2017, 06:52
2
14
00:00

Difficulty:

75% (hard)

Question Stats:

45% (01:19) correct 55% (02:02) wrong based on 160 sessions

### HideShow timer Statistics

In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.

A) 10
B) 15
C) 21
D) 28
E) 56

SOURCE: http://www.GMATinsight.com

_________________
Prosper!!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi

My Recent Posted Questions
Q-1-Integer-Divisibility l Q-2-Inequality DS l Q-3-Even/Odd l Q-4-Inequality

ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION
Math Expert
Joined: 02 Sep 2009
Posts: 62287
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

### Show Tags

16 May 2017, 07:50
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.

A) 10
B) 15
C) 21
D) 28
E) 56

SOURCE: http://www.GMATinsight.com

DISTRIBUTING ITEMS/PEOPLE/NUMBERS... (QUESTION COLLECTION):

https://gmatclub.com/forum/in-how-many- ... 87128.html
https://gmatclub.com/forum/in-how-many- ... 25669.html
https://gmatclub.com/forum/larry-michae ... 08739.html
https://gmatclub.com/forum/in-how-many- ... 26991.html
https://gmatclub.com/forum/in-how-many- ... 98697.html
https://gmatclub.com/forum/how-many-pos ... 85291.html
https://gmatclub.com/forum/how-many-way ... 37198.html
https://gmatclub.com/forum/in-how-many- ... 41072.html
https://gmatclub.com/forum/mrs-smith-ha ... 98225.html
https://gmatclub.com/forum/in-how-many- ... 70689.html
https://gmatclub.com/forum/in-how-many- ... 05384.html
https://gmatclub.com/forum/four-boys-pi ... 98701.html
https://gmatclub.com/forum/how-many-way ... 61598.html
https://gmatclub.com/forum/in-how-many- ... 73423.html
http://gmatclub.com/forum/in-how-many-w ... 41070.html
https://gmatclub.com/forum/in-how-many- ... 64389.html
https://gmatclub.com/forum/in-how-many- ... 33322.html
https://gmatclub.com/forum/in-how-many- ... 31187.html
https://gmatclub.com/forum/in-how-many- ... 06279.html
https://gmatclub.com/forum/in-how-many- ... 26348.html
https://gmatclub.com/forum/in-how-many- ... 81816.html
https://gmatclub.com/forum/in-how-many- ... 34223.html
https://gmatclub.com/forum/in-how-many- ... 40328.html
https://gmatclub.com/forum/in-how-many- ... 40329.html

HARD (FOR PRACTICE): https://gmatclub.com/forum/5-rings-on-4 ... 86111.html
_________________
Retired Moderator
Joined: 21 Aug 2013
Posts: 1369
Location: India
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

### Show Tags

26 Apr 2018, 10:23
4
5
Awamy wrote:
why the formula of identical objects doen'st work here ?
Is there any easy way to solve such problems please ?

Hello

The formula of identical objects DOES work here. If we have to distribute N identical objects among R distinct groups such that one or more people might get none of the objects, then the formula is = (N+R-1) C (R-1) (selecting R-1 objects out of N+R-1 objects)

BUT if N identical objects have to be distributed among R distinct groups such that everyone should get at least one object, then the formula is = (N-1) C (R-1) (selecting R-1 objects out of N-1 objects)

So in this question, since 6 identical chocolates have to be distributed among 3 distinct people, but everyone should get at least one, we will apply the second formula = (6-1) C (3-1) = 5C2 = 10, which is our answer
##### General Discussion
Senior Manager
Joined: 13 Oct 2016
Posts: 352
GPA: 3.98
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

### Show Tags

16 May 2017, 07:18
1
1
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.

A) 10
B) 15
C) 21
D) 28
E) 56

SOURCE: http://www.GMATinsight.com

Hi

# of chocolates distributed to each child -$$x_1, x_2, x_3$$, where $$x_i > 0$$

We have non-empty set:

$$x_1 + x_2 + x_3 = 6$$

We need to convert it into $$x_i >=0$$ substituting each $$x_i$$ with $$y_i = x_i - 1$$.

$$x_i = y_i +1$$:

$$y_1 + y_2 + y_3 = 3$$

$$_{3+3-1}C_3 = _5C_3 = \frac{5*4}{2} = 10$$

Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 260
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

### Show Tags

09 Jan 2018, 10:19
2
1
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.

A) 10
B) 15
C) 21
D) 28
E) 56

SOURCE: http://www.GMATinsight.com
\\

since a child must get at least 1 chocolate, lets distribute 1 chocolate to each child first, and thus we are left with 3 chocolates to redistribute

since chocolates are identical, the remaining 3 chocolates can be distributed among 3 children as follows

5!
_____
3! 2!

hope this helps
thanks

cheers, and do consider some kudos, guys
Intern
Joined: 20 Nov 2017
Posts: 4
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

### Show Tags

26 Apr 2018, 08:02
why the formula of identical objects doen'st work here ?
Is there any easy way to solve such problems please ?
Director
Joined: 20 Sep 2016
Posts: 661
Location: India
Concentration: Strategy, Operations
GPA: 3.6
WE: Operations (Consumer Products)
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

### Show Tags

17 Dec 2018, 05:21
chetan2u Bunuel could you please explain how to solve this without (n-1)Cr-1 ... i wanna learn the concept
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 6057
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

### Show Tags

28 Jul 2019, 01:58
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.

A) 10
B) 15
C) 21
D) 28
E) 56

SOURCE: http://www.GMATinsight.com

formula to use here we can take case that child may get 0 chocolate
n-1Cr-1 ; n=6 . r= 3
5c2; 10
IMO A
VP
Joined: 24 Nov 2016
Posts: 1342
Location: United States
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

### Show Tags

26 Aug 2019, 13:02
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.

A) 10
B) 15
C) 21
D) 28
E) 56

SOURCE: http://www.GMATinsight.com

given: 6 identical chocs, 3 different kids, at least 1 each;

$$k_1+k_2+k_3=6…(k_1'+1)+(k_2+1)+(k_3+1)=6…k_1'+k_2+k_3=3$$
$$C(n+r-1,r-1)=(3+3-1,3-1)=\frac{5!}{2!3!}=10$$

CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3396
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

### Show Tags

28 Feb 2020, 23:10
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.

A) 10
B) 15
C) 21
D) 28
E) 56

SOURCE: http://www.GMATinsight.com

The detailed solution to the above problem using two methods is explained in the attached video

_________________
Prosper!!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi

My Recent Posted Questions
Q-1-Integer-Divisibility l Q-2-Inequality DS l Q-3-Even/Odd l Q-4-Inequality

ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION
Re: In how many ways can 6 chocolates be distributed among 3 children? A c   [#permalink] 28 Feb 2020, 23:10
Display posts from previous: Sort by