R a marked ball into n different boxes, asking for no empty box, ask how many different distribution options?

By test instructions can know r>=n, I originally thought is first to take n all permutations, the remaining r-n each has n in the choice, so the result is n!*n^ (r-n). God guesses that this will be repeated. For example, 1 to 5 balls, ABC three boxes, MSPaint open the artboard.

C Box first put 5 and put 2 (345, after C square 2;342 after C Party 5), so repeat.

Allowed to repeat the combination is C (n+r-1,r), allowing the repetition of the arrangement with the exponential type of the parent function.

R a marked ball into n different boxes, asking for no empty box, ask how many different distribution options?