You need to count the number of ways to represent 18 as a sum of 6 natural numbers (possibly equal to zero). See this Wiki page.
How many different ways can the sweets be divided among 6 kids so that each of them receives atleast 3 sweets?
Firstly I'd give each of them 3 sweets, a total of 18.
Then distribute the other 18 any way possible? Not sure how to go about that though?
Thanks in advance for any help.
Ok I did something similar. Here's what I got:
If you had to find the number of different ways that 36 identical sweets can be divided among 6 kids it would 41Choose5 so the answer is 749,398.
Ofcourse I want each of the kids to have atleast 3 sweets. So I'd say the answer to my original question is 23Choose5 = 33,649.
Is that right?
Hello, Markhor!
How many different ways can 36 sweets be divided among 6 kids
so that each of them receives atl east 3 sweets?
Firstly I'd give each of them 3 sweets, a total of 18.
Then distribute the other 18 any way possible? . Yes!
We will distribute the other 18 sweets among the 6 kids.
For each sweet, we have 6 choices of kids to give it to.
So there are: . possible distributions.
. . Edit: This is wrong! . . . *blush*
There are: . distributions.
It is reasonable to assume that children are numbered but sweets are not. In fact, the OP says that the sweets are identical.
Now, is the set of all 18-tuples where for each . Each says to which kid the th sweet goes. However, since sweets are identical, we don't care whether sweets #1 through 9 go to kid #1 and those #10 through 18 go to kid #2 or vice versa. So, in our model we count not the number of ordered tuples, but the number of multisets . This is .