Someone shot 10 arrows at a target with 10 concentric rings, each being worth a different integer number of points from 1 to 10. How many different ways are there of scoring 10 points by doing this? (Note that not all the arrows have to hit the target and that order matters; 6 first then 4 is different from 4 first then 6. Also note that two or more arrows may hit the same ring.)

(In reply to re(3): Intuitive Representation IMHO (spoilers) by David Shin)

Um, ok, but I don’t think either one of our solutions needed to be proven by anything else. I think they are both solid proofs on their own.

And second, there are 4 existing formulas for n choose r "permutations with replacement," "permutations without replacement," "combinations with replacement," and "combinations without replacement." So the formula wasn’t being proven, it was just being used once I showed what kind of situation my representation fell under.

Posted by nikki on 2004-09-24 11:17:24