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

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CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2722
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

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16 May 2017, 06:49
00:00

Difficulty:

35% (medium)

Question Stats:

64% (01:17) correct 36% (02:21) wrong based on 113 sessions

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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

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Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

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16 May 2017, 07:50
2
4
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

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##### General Discussion
Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

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16 May 2017, 07:06
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)

$$x_1 + x_2 + x_3 = 6$$

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

Director
Joined: 21 Mar 2016
Posts: 523
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

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16 May 2017, 09:35
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
Director
Joined: 14 Nov 2014
Posts: 632
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]

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16 May 2017, 09:46
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
Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 272
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

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09 Jan 2018, 08:15
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

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
Intern
Joined: 15 Aug 2017
Posts: 14
Re: In how many ways can 6 chocolates be distributed among 3 children? A c  [#permalink]

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10 Jan 2018, 00:32
Using stick method,

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

So B
Re: In how many ways can 6 chocolates be distributed among 3 children? A c &nbs [#permalink] 10 Jan 2018, 00:32
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# In how many ways can 6 chocolates be distributed among 3 children? A c

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