GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Nov 2019, 06:33

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

Show Tags

New post 16 May 2017, 07:49
18
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

52% (01:26) correct 48% (02:02) wrong based on 166 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 0 to 6 and all the chocolates are identical.

A) 21
B) 28
C) 56
D) 112
E) 224

SOURCE: http://www.GMATinsight.com

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

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59229
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

Show Tags

New post 16 May 2017, 08:50
2
5
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 0 to 6 and all the chocolates are identical.

A) 21
B) 28
C) 56
D) 112
E) 224

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
_________________
General Discussion
Senior Manager
Senior Manager
User avatar
G
Status: love the club...
Joined: 24 Mar 2015
Posts: 265
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

Show Tags

New post 09 Jan 2018, 09:15
3
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 0 to 6 and all the chocolates are identical.

A) 21
B) 28
C) 56
D) 112
E) 224

SOURCE: http://www.GMATinsight.com


hi

since chocolates are identical, and there are 3 children, we can think this way

c | c | c c c c

thus

8!
______
6! 2!

= 28, the answer
thanks

cheers, and do consider some kudos, guys
:cool:
Senior Manager
Senior Manager
avatar
S
Joined: 21 Mar 2016
Posts: 495
Reviews Badge
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

Show Tags

New post 16 May 2017, 10:35
1
can be solve using stick method,,
imagine 2 sticks and 6 choclates ..
so.. it wud luk like this ||CCCCCC

permutation of the above = (8!/2! 6!) = 28

ans B
Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 356
GPA: 3.98
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

Show Tags

New post 16 May 2017, 08:06
1
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 0 to 6 and all the chocolates are identical.

A) 21
B) 28
C) 56
D) 112
E) 224

SOURCE: http://www.GMATinsight.com


Hi

Multichoosing problem.

We need to distribute 6 identical chocolates among 3 children: (\(x_1, x_2, x_3\) - # each one will get)

\(x_1 + x_2 + x_3 = 6\)

\(_{3+6-1}C_6 = _8C_6 = _8C_2 = \frac{8*7}{2} = 28\)

Answer B
Director
Director
avatar
P
Joined: 14 Nov 2014
Posts: 593
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

Show Tags

New post 16 May 2017, 10:46
1
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 0 to 6 and all the chocolates are identical.

A) 21
B) 28
C) 56
D) 112
E) 224

SOURCE: http://www.GMATinsight.com


i took a bit long route -
3 +ve digit that can sum to 6
006-3 ways
051-6 ways
411-3 ways
321-6 ways
330- 3 ways
222- 1 way
204- 6 ways

total- 28 ways
Intern
Intern
avatar
B
Joined: 15 Aug 2017
Posts: 12
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

Show Tags

New post 10 Jan 2018, 01:32
Using stick method,

permutation of the above = (8!/2! 6!) = 28

So B
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

Show Tags

New post 23 Jul 2019, 10:29
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 0 to 6 and all the chocolates are identical.

A) 21
B) 28
C) 56
D) 112
E) 224

SOURCE: http://www.GMATinsight.com


Let, three children get a, b and c chocolates respectively

i.e. a+b+c = 6

Now, the whole number solutions of an equation = (n+r-1)C(r-1) = (6+3-1)C(3-1) = 8C2 = 28

Answer: Option B

ALTERNATIVE

Let, three children get a, b and c chocolates respectively

i.e. a+b+c = 6

@a=0, (b,c) can be (0,6) (1,5) (2,4) (3,3) (4,2) (5,1) (6,0) i.e. 7 ways
@a=1, (b,c) can be (0,5) (1,4) (2,3) (3,2) (4,1) (5,0) i.e. 6 ways
@a=2, (b,c) can be (0,4) (1,3) (2,2) (3,1) (4,0) i.e. 5 ways
and so on...

Total Ways of distribution = 7+6+5+4+3+2+1 = 28

Answer: Option B


To attend the !!!FREE!!! Live class on Permutation and combination on 24th July 2019 @9 PM IST, click and register on the LINK

.
;
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Intern
avatar
B
Joined: 16 Jul 2019
Posts: 5
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

Show Tags

New post 25 Jul 2019, 07:13
Can someone explain the stick method, please?
Manager
Manager
avatar
B
Joined: 20 Apr 2019
Posts: 108
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

Show Tags

New post 28 Jul 2019, 08:22
vitaliyGMAT wrote:
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 0 to 6 and all the chocolates are identical.

A) 21
B) 28
C) 56
D) 112
E) 224

SOURCE: http://www.GMATinsight.com


Hi

Multichoosing problem.

We need to distribute 6 identical chocolates among 3 children: (\(x_1, x_2, x_3\) - # each one will get)

\(x_1 + x_2 + x_3 = 6\)

\(_{3+6-1}C_6 = _8C_6 = _8C_2 = \frac{8*7}{2} = 28\)

Answer B

Why 3+6-1? Can someone explain please?
Manager
Manager
avatar
B
Joined: 20 Apr 2019
Posts: 108
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

Show Tags

New post 01 Aug 2019, 05:08
GMATinsight wrote:
GMATinsight wrote:
In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 0 to 6 and all the chocolates are identical.

A) 21
B) 28
C) 56
D) 112
E) 224

SOURCE: http://www.GMATinsight.com


Let, three children get a, b and c chocolates respectively

i.e. a+b+c = 6

Now, the whole number solutions of an equation = (n+r-1)C(r-1) = (6+3-1)C(3-1) = 8C2 = 28

Answer: Option B

ALTERNATIVE

Let, three children get a, b and c chocolates respectively

i.e. a+b+c = 6

@a=0, (b,c) can be (0,6) (1,5) (2,4) (3,3) (4,2) (5,1) (6,0) i.e. 7 ways
@a=1, (b,c) can be (0,5) (1,4) (2,3) (3,2) (4,1) (5,0) i.e. 6 ways
@a=2, (b,c) can be (0,4) (1,3) (2,2) (3,1) (4,0) i.e. 5 ways
and so on...

Total Ways of distribution = 7+6+5+4+3+2+1 = 28

Answer: Option B


To attend the !!!FREE!!! Live class on Permutation and combination on 24th July 2019 @9 PM IST, click and register on the LINK

.
;

Hello, can you please explain why the whole number solutions of the equation = (n+r-1)C(r-1)?
Thank you
GMAT Club Bot
Re: In how many ways can 6 chocolates be distributed among 3 children? A c   [#permalink] 01 Aug 2019, 05:08
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne