If I want to know how many ways there are to distribute 11 chocolate chip cookies to 50 children, is there any way to do this without brute force?
You mixed up the things my friend.ok so you want combinations with reptition then, which is towards the bottom of the wiki page
this site has a reasonable explanation of how to derive the formula at teh very end of the page
You are right. Sorry for misunderstanding you.Hi njama, not sure what you mean was mixed up?
When referring to ordering, I was implying the cookies are indistinguishable for all intents and purposes (ie. receieving a cookie is the same as receiving any other cookie). This makes it a combination rather than permutation question.
As you and jimmianlin point out, recieving 2 cookies is clearly different from recieving 1 cookie... You could treat this with a repetitive approach of working out the combinations of each cookie distribution, as you have done, but this will become difficult with large cookie/children numbers
That leads you to looking at combinations with repetition (see previous website for good explanation)
In your case
n = 5 number of children
r = 3 number of cookies
(n-1+r)!/((n-1)!r!) = 7!/(4!3!) = 7.5 = 35, agreeing with your work
I feel like a cookie after all this...