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

Question

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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rajdeep212003 · Answer

At first I was thinking about using 7C3, but that would only work if we were selecting 3 chocolates from 7.

Here every chocolate can go to any of the 3 children.

So for each chocolate, there are 3 possible choices.

That means:

3 × 3 × 3 × 3 × 3 × 3 × 3 
= 37 
= 2187

So answer should be Option E.

The main thing here is:
this is distribution, not selection.

– Rajdeep

Adit_ · Answer

The chocolates can be distributed in 3^7 ways =  2187 .

Answer:  Option E

BongBideshini · Answer

Since all 7 chocolates are  distinct and independent :
Total ways =
 3 × 3 × 3 × 3 × 3 × 3 × 3
 =  3^7 
=  2187

ExpertsGlobal5 · Answer

E is the correct answer choice.

Video explanation:

https://www.youtube.com/watch?v=DjH2lqPrZzk

suntprovident · Answer

If any number of chocolates can be distributed why is 0 not a possibility and accordingly the answer should be 4^7 ?

Bunuel · Answer

3^7 already includes the cases in which one child or even two children get 0 chocolates.

For each chocolate, there are only 3 choices: give it to child 1, child 2, or child 3.

0 chocolates for a child happens automatically when none of the 7 chocolates is assigned to that child.

So we do not need a fourth choice.

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