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# In how many ways can 7 different chocolates be distributed among 3

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Manager
Joined: 07 Jun 2017
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Location: India
Concentration: Technology, General Management
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In how many ways can 7 different chocolates be distributed among 3  [#permalink]

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18 Oct 2017, 02:56
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Difficulty:

55% (hard)

Question Stats:

55% (01:23) correct 45% (02:03) wrong based on 88 sessions

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In how many ways can 7 different chocolates be distributed among 3 children if each child can get any number of chocolates?

A. 35
B. 84
C. 120
D. 210
E. 2187

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Re: In how many ways can 7 different chocolates be distributed among 3  [#permalink]

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18 Oct 2017, 06:54
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nkmungila wrote:
In how many ways can 7 different chocolates be distributed among 3 children if each child can get any number of chocolates?

A. 35
B. 84
C. 120
D. 210
E. 2187

Every chocolate can be given to any $$3$$ children. Thus number of ways a chocolate can be distributed is $$3$$

so $$7$$ chocolates can be distributed in $$=3*3*3*3*3*3*3=3^7=2187$$

Option E
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Re: In how many ways can 7 different chocolates be distributed among 3  [#permalink]

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18 Oct 2017, 09:43
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The first chocolate can be distributed to 1 out of 3 children => there are 3 ways to distribute the first chocolate
The second chocolate can be distributed to 1 out of 3 children => there are 3 ways to distribute the second chocolate
The same explanation for 3rd, 4th, 5th, 6th and 7th chocolate

So, there are: 3x3x3x...x3 = 3^7 ways to distribute chocolate. Answer E

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Re: In how many ways can 7 different chocolates be distributed among 3  [#permalink]

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22 Oct 2017, 16:54
nkmungila wrote:
In how many ways can 7 different chocolates be distributed among 3 children if each child can get any number of chocolates?

A. 35
B. 84
C. 120
D. 210
E. 2187

Since each chocolate can be given to any one of the 3 children, there are 3 choices for the first chocolate to be distributed, 3 choices for the second chocolate to be distributed, etc. Thus, the total number of ways these 7 chocolates can be distributed is:

3 x 3 x 3 x 3 x 3 x 3 x 3 = 3^7

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Re: In how many ways can 7 different chocolates be distributed among 3  [#permalink]

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06 Aug 2019, 17:48
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Re: In how many ways can 7 different chocolates be distributed among 3   [#permalink] 06 Aug 2019, 17:48
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