GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 05 Dec 2019, 12:51

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 25 Dec 2016
Posts: 3
in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

### Show Tags

Updated on: 06 Feb 2019, 08:58
18
00:00

Difficulty:

65% (hard)

Question Stats:

44% (01:18) correct 56% (01:29) wrong based on 176 sessions

### HideShow timer Statistics

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, 11:12.
Last edited by Bunuel on 06 Feb 2019, 08:58, edited 2 times in total.
Renamed the topic.
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4835
Location: India
GPA: 3.5
Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

### Show Tags

25 Dec 2016, 13:49
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...
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
##### General Discussion
Intern
Joined: 25 Dec 2016
Posts: 3
Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

### Show Tags

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...
Intern
Joined: 21 May 2016
Posts: 27
Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

### Show Tags

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
Intern
Joined: 27 Aug 2018
Posts: 3
Location: United States
Schools: Kelley (A)
GMAT 1: 620 Q32 V38
GPA: 3.56
Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

### Show Tags

30 Sep 2018, 06:37
Having the answer in the OG post is not helpful to people using these questions to study.
Retired Moderator
Joined: 11 Aug 2016
Posts: 367
Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

### Show Tags

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.

Senior Manager
Joined: 21 Jun 2017
Posts: 321
Location: India
Concentration: Finance, Economics
Schools: IIM
GPA: 3
WE: Corporate Finance (Commercial Banking)
Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

### Show Tags

13 Oct 2018, 06:19
Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

### Show Tags

06 Feb 2019, 07:34
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
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Director
Joined: 12 Feb 2015
Posts: 956
Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

### Show Tags

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

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
_________________
________________
Manish

"Only I can change my life. No one can do it for me"
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8610
Location: United States (CA)
Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

### Show Tags

06 Aug 2019, 18:13
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

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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Joined: 28 Feb 2014
Posts: 202
Location: India
GPA: 3.97
WE: Engineering (Education)
Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

### Show Tags

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
Senior Manager
Joined: 25 Sep 2018
Posts: 466
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30
GPA: 3.97
WE: Investment Banking (Investment Banking)
Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

### Show Tags

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
_________________
Why do we fall?...So we can learn to pick ourselves up again
Intern
Joined: 27 Aug 2019
Posts: 5
Re: in how many ways 5 different chocolates be distributed to 4 children  [#permalink]

### Show Tags

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

Posted from my mobile device
Re: in how many ways 5 different chocolates be distributed to 4 children   [#permalink] 20 Sep 2019, 10:26
Display posts from previous: Sort by