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# in how many ways 5 different chocolates be distributed to 4 children

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Joined: 25 Dec 2016
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in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

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Updated on: 06 Feb 2019, 07:58
11
00:00

Difficulty:

55% (hard)

Question Stats:

48% (01:16) correct 52% (01:20) wrong based on 116 sessions

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In how many ways 5 different chocolates be distributed to 4 children such that any child can get any number of chocolates?

A. 20
B. 24
C. 120
D. 625
E. 1024

I saw this question on a youtube video and the solution showed 4*4*4*4*4 = 1024, but i was thinking it would be 5*5*5*5 and this answer isn't even in the options. Please help me understand this.

Originally posted by Dennis03 on 25 Dec 2016, 10:12.
Last edited by Bunuel on 06 Feb 2019, 07:58, edited 2 times in total.
Renamed the topic.
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Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

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25 Dec 2016, 12:49
3
3
Dennis03 wrote:
in how many ways 5 different chocolates be distributed to 4 children such that any child can get any number of chocolates?

1) 20
2) 24
3) 120
4) 625
5) 1024

I saw this question on a youtube video and the solution showed 4*4*4*4*4 = 1024, but i was thinking it would be 5*5*5*5 and this answer isn't even in the options. Please help me understand this.

Let the 5 cholcolates be : $$C_1$$ , $$C_2$$ , $$C_3$$ , $$C_4$$ & $$C_5$$
And there be 4 Students : $$S_1$$ , $$S_2$$, $$S_3$$ & $$S_4$$

Now, The first Chocolate can be given in 4 ways ( Either to $$S_1$$ or $$S_2$$ or $$S_3$$ or $$S_4$$ )
The Second Chocolate can be given in 4 ways ( Either to $$S_1$$ or $$S_2$$ or $$S_3$$ or $$S_4$$ )
The Third Chocolate can be given in 4 ways ( Either to $$S_1$$ or $$S_2$$ or $$S_3$$ or $$S_4$$ )
The Fourth Chocolate can be given in 4 ways ( Either to $$S_1$$ or $$S_2$$ or $$S_3$$ or $$S_4$$ )
The fifth Chocolate can be given in 4 ways ( Either to $$S_1$$ or $$S_2$$ or $$S_3$$ or $$S_4$$ )

Hence, the total No of ways possible is $$4^5$$ = $$1024$$

Hence, answer will be (E) 1024...
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##### General Discussion
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Joined: 25 Dec 2016
Posts: 2
Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

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26 Dec 2016, 10:50
Thanks a lot Abhishek!

Abhishek009 wrote:
Dennis03 wrote:
in how many ways 5 different chocolates be distributed to 4 children such that any child can get any number of chocolates?

1) 20
2) 24
3) 120
4) 625
5) 1024

I saw this question on a youtube video and the solution showed 4*4*4*4*4 = 1024, but i was thinking it would be 5*5*5*5 and this answer isn't even in the options. Please help me understand this.

Let the 5 cholcolates be : $$C_1$$ , $$C_2$$ , $$C_3$$ , $$C_4$$ & $$C_5$$
And there be 4 Students : $$S_1$$ , $$S_2$$, $$S_3$$ & $$S_4$$

Now, The first Chocolate can be given in 4 ways ( Either to $$S_1$$ or $$S_2$$ or $$S_3$$ or $$S_4$$ )
The Second Chocolate can be given in 4 ways ( Either to $$S_1$$ or $$S_2$$ or $$S_3$$ or $$S_4$$ )
The Third Chocolate can be given in 4 ways ( Either to $$S_1$$ or $$S_2$$ or $$S_3$$ or $$S_4$$ )
The Fourth Chocolate can be given in 4 ways ( Either to $$S_1$$ or $$S_2$$ or $$S_3$$ or $$S_4$$ )
The fifth Chocolate can be given in 4 ways ( Either to $$S_1$$ or $$S_2$$ or $$S_3$$ or $$S_4$$ )

Hence, the total No of ways possible is $$4^5$$ = $$1024$$

Hence, answer will be (E) 1024...
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Joined: 21 May 2016
Posts: 28
Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

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29 Sep 2018, 23:28
This is a typical example of chocolates going to children. So each chocolate has 4 options and total 5 children. Hence 4^5
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Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

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30 Sep 2018, 05:37
Having the answer in the OG post is not helpful to people using these questions to study.
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Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

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30 Sep 2018, 12:07
2
Dennis03 wrote:
in how many ways 5 different chocolates be distributed to 4 children such that any child can get any number of chocolates?

1) 20
2) 24
3) 120
4) 625
5) 1024

Lets denote Chocolates by C

So we can distribute C1 in 4 ways
C2-4 ways
C3-4 ways
C4-4 ways
C5-4 ways

Total no of ways of distribution: 4*4*4*4*4
=4^5

An easy way without actually calculating the answer would be to check out he last digit.
Even Powers of 4 yield 4 as unit's digit.
Odd powers of 4 yield 6 as units digit.

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Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

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13 Oct 2018, 05:19
https://gmatclub.com/forum/5-rings-on-4 ... er#p649557

check this out
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Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

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06 Feb 2019, 06:34
Dennis03 wrote:
in how many ways 5 different chocolates be distributed to 4 children such that any child can get any number of chocolates?

1) 20
2) 24
3) 120
4) 625
5) 1024

Another example of players^occurrence

(4)^5

1024

E
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Re: in how many ways 5 different chocolates be distributed to 4 children   [#permalink] 06 Feb 2019, 06:34
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