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

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Dennis03
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in how many ways 5 different chocolates be distributed to 4 children [#permalink] New post   Updated on: 06 Feb 2019, 08:58
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E

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65% (hard)

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45% (01:13) correct 55% (01:30) wrong based on 337 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

Show Spoiler
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.
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E

Originally posted by Dennis03 on 25 Dec 2016, 11:12.
Last edited by Bunuel on 06 Feb 2019, 08:58, edited 2 times in total.
Renamed the topic.
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Abhishek009
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Re: in how many ways 5 different chocolates be distributed to 4 children [#permalink] 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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Dennis03
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Re: in how many ways 5 different chocolates be distributed to 4 children [#permalink] 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] 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] 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] New post   30 Sep 2018, 13:07
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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


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] New post   13 Oct 2018, 06:19
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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] New post   06 Feb 2019, 07:34
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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


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] New post   26 Apr 2019, 23:21
Dennis03 wrote:
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

Show Spoiler
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.


The number of ways in which 5 different chocolates be distributed to 4 children such that any child can get any number of chocolates is 4 * 4 * 4 * 4 * 4 = 1024. Option E is the correct answer
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Re: in how many ways 5 different chocolates be distributed to 4 children [#permalink] New post   06 Aug 2019, 18:13
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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?

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

Show Spoiler
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.


Since each chocolate can be given to any of the 4 children, each of the 5chocolates has 4 choices. So the total number of ways is 4 x 4 x 4 x 4 x 4 = 4^5 = 1024.

Answer: 5
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Re: in how many ways 5 different chocolates be distributed to 4 children [#permalink] New post   06 Aug 2019, 21:36
1st chocolate can be given in 4 ways
2nd can also be given in 4 ways
similarly 3rd, 4th and 5th can be given in 4 ways each
So total ways to give chocolate = 4^5 = 1024

E is correct
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Re: in how many ways 5 different chocolates be distributed to 4 children [#permalink] New post   06 Aug 2019, 21:51
Each chocolate is distributed in 4 ways and hence if there are 5 children, it will b 4 X 4 X 4 X 4 X 4 = 1024
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Re: in how many ways 5 different chocolates be distributed to 4 children [#permalink] New post   20 Sep 2019, 10:26
Let the 5 cholcolates be : C1C1 , C2C2 , C3C3 , C4C4 & C5C5
And there be 4 Students : S1S1 , S2S2, S3S3 & S4S4

Now, The first Chocolate can be given in 4 ways ( Either to S1S1 or S2S2 or S3S3 or S4S4 )
The Second Chocolate can be given in 4 ways ( Either to S1S1 or S2S2 or S3S3 or S4S4 )
The Third Chocolate can be given in 4 ways ( Either to S1S1 or S2S2 or S3S3 or S4S4 )
The Fourth Chocolate can be given in 4 ways ( Either to S1S1 or S2S2 or S3S3 or S4S4 )
The fifth Chocolate can be given in 4 ways ( Either to S1S1 or S2S2 or S3S3 or S4S4 )

Hence, the total No of ways possible is 4545 = 1024

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Re: in how many ways 5 different chocolates be distributed to 4 children [#permalink] New post   28 Aug 2023, 05:48
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Re: in how many ways 5 different chocolates be distributed to 4 children [#permalink]
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