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

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

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New post Updated on: 25 Dec 2016, 11:16
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E

Difficulty:

  55% (hard)

Question Stats:

59% (00:37) correct 41% (00:57) wrong based on 128 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?

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.

Originally posted by Dennis03 on 25 Dec 2016, 11:12.
Last edited by Bunuel on 25 Dec 2016, 11:16, edited 1 time 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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New post 25 Dec 2016, 13:49
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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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Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

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New post 26 Dec 2016, 11:50
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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Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

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New post 30 Sep 2018, 00:28
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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New post 30 Sep 2018, 06:37
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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New post 30 Sep 2018, 13:07
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.

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

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New post 13 Oct 2018, 06:19
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 &nbs [#permalink] 13 Oct 2018, 06:19
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