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  • How many different ways are there to distribute 12 identical bags among 6 children so that each one gets at least one and never more than five?  <div class='qna-option'

How many different ways are there to distribute 12 identical bags among 6 children so that each one gets at least one and never more than five?

 

Option: 1

1100


Option: 2

1300


Option: 3

1200

 


Option: 4

1500


Answers (1)

best_answer

Take the distribution of 12 identical bags among 6 children.

  a + b + c + d + e + f = 12

Every child receives one bag, so a + b + c + d + e + f = 6

Any child can now only receive four bags.

There may be 3 situations. 2, 2, 1, 0, 0, 0 which can be represented in  \frac{6!}{2!2!}=120

Similarly, another case is 2, 1, 1, 1, 0, 0 which can be represented in  \frac{6!}{2!}=360

Similarly, another case is 1, 1, 1, 1, 0, 0 which can be represented in  {6!}=720

Thus, 

120+360+720=1200

Therefore, there are 1200 ways to distribute 8 identical pens among 5 children such that each child receives at least one pen but not more than three pens.

 

 

 

Posted by

Shailly goel

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