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(a) How many distinct 6-tuples of positive integers (a1,...,a6) are there such that a1+...+a6 = 14?

(b) How many distinct 6-tuples of nonnegative integers (a1,...,a6) are there such that a1+...+a6 = 14?

I'm thinking the only difference between (a) and (b) is that 0 is not allowed in (a)

Joseph Quinsey
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user3003255
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  • You are correct about the difference between (a) and (b). (b) is a standard stars and bars problem. For (a), simply set the condition beforehand that each of $a_{1}, \ldots, a_{6}$ is at least $1$. Then, the problem is a standard stars and bars problem of distributing $8$ apples to 6 people, allowing a person to receive $0$ apples. – Alex Wertheim Dec 03 '13 at 20:41
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    That is correct. Have you looked at stars and bars? – Ross Millikan Dec 03 '13 at 20:41
  • Thanks, looking into stars and bars now. – user3003255 Dec 03 '13 at 21:01

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