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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
Posts: 1955
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In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]

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16 May 2017, 06:52
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Difficulty:

95% (hard)

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38% (01:13) correct 62% (01:01) wrong based on 69 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 1 to 6 and all the chocolates are identical.

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

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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16 May 2017, 07:18
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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 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 $$y_i = x_i - 1$$.

$$x_i = y_i +1$$:

$$y_1 + y_2 + y_3 = 3$$

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

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Joined: 02 Sep 2009
Posts: 43810
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
Expert's post
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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 1 to 6 and all the chocolates are identical.

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

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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09 Jan 2018, 10:19
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
now we are in business

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

5!
_____
3! 2!

= 10, the answer

hope this helps
thanks

cheers, and do consider some kudos, guys
Re: In how many ways can 6 chocolates be distributed among 3 children? A c   [#permalink] 09 Jan 2018, 10:19
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# In how many ways can 6 chocolates be distributed among 3 children? A c

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