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(2): Intuitive Representation IMHO (spoilers) by nikki)

You can think of my solution as having proved your statement:

"So for combinations with replacement, the formula for 11 choose 9 is (11+9-1)!/[9!*(11-1)!]."

I guess if you already know the formula, you stop there.