- #1
jimmianlin
- 3
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Homework Statement
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?
lanedance said: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
http://www.mathsisfun.com/combinatorics/combinations-permutations.html
lanedance said: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, receiving 2 cookies is clearly different from receiving 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...
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