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

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Joined: 08 Jul 2010
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In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]

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New post 16 May 2017, 06:49
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  55% (hard)

Question Stats:

54% (26:48) correct 46% (01:58) wrong based on 87 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
[Reveal] Spoiler: OA

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

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New post 16 May 2017, 07:06
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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
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]

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New post 16 May 2017, 07:50
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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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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]

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

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

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New post 09 Jan 2018, 08:15
1
This post received
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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:
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Joined: 15 Aug 2017
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]

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New post 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   [#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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