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

niks18 · Accepted Answer

Every chocolate can be given to any  3  children. Thus number of ways a chocolate can be distributed is  3

so  7  chocolates can be distributed in  =3*3*3*3*3*3*3=3^7=2187

Option  E

mbaapplicant2019 · Answer

The first chocolate can be distributed to 1 out of 3 children => there are 3 ways to distribute the first chocolate
The second chocolate can be distributed to 1 out of 3 children => there are 3 ways to distribute the second chocolate
The same explanation for 3rd, 4th, 5th, 6th and 7th chocolate

So, there are: 3x3x3x...x3 = 3^7 ways to distribute chocolate. Answer E

Please kudo if it helps. Thanks

ScottTargetTestPrep · Answer

Since each chocolate can be given to any one of the 3 children, there are 3 choices for the first chocolate to be distributed, 3 choices for the second chocolate to be distributed, etc. Thus, the total number of ways these 7 chocolates can be distributed is:

3 x 3 x 3 x 3 x 3 x 3 x 3 = 3^7

Answer: E

exc4libur · Answer

METHOD: SHORT
 3^7=2187

METHOD: LONG
700; 3!/2! (00 are identical) x 7c7 = 3x1 = 3
610; 3! x 7c6 = 6x7 = 42
520; 3! x 7c5 = 6x21 = 126 
511; 3! x 7c5 = 6x21 = 126
430; 3! x 7c4 = 6x35 = 210
421; 3! x 7c4 x 3c2 = 6x35x3 = 630
331; 3!/2! (double counting) x 7c3 x 4c3 = 3x35x4 = 420
322; 3!/2! (double counting) x 7c3 x 4c2 = 3x35x6 = 630
total; 3+42+126(2)+210+420+630(2)=2187

Answer (E)

kt22 · Answer

Hey, can we use the partition method in this question?

TIA

Shrey1 · Answer

Hey  kt22

Stars and Bar partitioning method can't be applied to this problem because we are not distributing identical objects in this case, the question mentions 7 different chocolates.

When distributing identical objects, we should use the "Stars and Bars" method.

Utkersh · Answer

Apologies, I'm a bit weak in this topic. Why is it that we are not considering the case in which the chocolate is not being distributed to any child. It is mentioned that the children can get ANY NUMBER of chocolates so does this not include 0? And hence, for each chocolate, there would now be 4 choices, either it will go to child 1, child 2, chilld 3 or no child at all.

Bunuel · Answer

The phrase "chocolates must be distributed among 3 children" means that all chocolates must be given out to one or more of the three children. A chocolate doesn't have the option of not being distributed; it has to be given to either child 1, child 2, or child 3. So, we can have a case when one or two children are not getting any chocolate but not the case when all three get 0, because after all the chocolates must be distributed AMONG them. Therefore, there are 3 choices for each chocolate, resulting in 3^7 total combinations.

bumpbot · Answer

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

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

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