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?
1100
1300
1200
1500
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
Similarly, another case is 2, 1, 1, 1, 0, 0 which can be represented in
Similarly, another case is 1, 1, 1, 1, 0, 0 which can be represented in
Thus,
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.
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