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

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nkmungila
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In how many ways can 7 different chocolates be distributed among 3 [#permalink] New post  18 Oct 2017, 02:56
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65% (hard)

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53% (01:30) correct 47% (01:49) wrong based on 349 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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niks18
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Re: In how many ways can 7 different chocolates be distributed among 3 [#permalink] New post  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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mbaapplicant2019
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Re: In how many ways can 7 different chocolates be distributed among 3 [#permalink] New post  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

Please kudo if it helps. Thanks
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ScottTargetTestPrep
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Re: In how many ways can 7 different chocolates be distributed among 3 [#permalink] New post  22 Oct 2017, 16:54
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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


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

Answer: E
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exc4libur
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Re: In how many ways can 7 different chocolates be distributed among 3 [#permalink] New post  26 Aug 2019, 16:38
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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


METHOD: SHORT
\(3^7=2187\)

METHOD: LONG
700; 3!/2! (00 are identical) x 7c7 = 3x1 = 3
610; 3! x 7c6 = 6x7 = 42
520; 3! x 7c5 = 6x21 = 126
511; 3! x 7c5 = 6x21 = 126
430; 3! x 7c4 = 6x35 = 210
421; 3! x 7c4 x 3c2 = 6x35x3 = 630
331; 3!/2! (double counting) x 7c3 x 4c3 = 3x35x4 = 420
322; 3!/2! (double counting) x 7c3 x 4c2 = 3x35x6 = 630
total; 3+42+126(2)+210+420+630(2)=2187

Answer (E)
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kt22
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Re: In how many ways can 7 different chocolates be distributed among 3 [#permalink] New post  27 Oct 2019, 02:25
Hey, can we use the partition method in this question?

TIA
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Shrey1
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Re: In how many ways can 7 different chocolates be distributed among 3 [#permalink] New post  06 Mar 2024, 20:13
Hey kt22

Stars and Bar partitioning method can't be applied to this problem because we are not distributing identical objects in this case, the question mentions 7 different chocolates.

When distributing identical objects, we should use the "Stars and Bars" method.
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Re: In how many ways can 7 different chocolates be distributed among 3 [#permalink]
06 Mar 2024, 20:13
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