I'm trying to answer this question for an RPG game. The player (or the GM) has to roll $N$ 10-sided dice and then she has to form groups that sum at least 10 (I'll call them Raises, using the game term).
As an example, if I roll 3d10 and get 10, 7 and 3, I get two Raises: {10}, {7,3}. If I roll 3d10 and get 2, 9 and 9, I get only one Raise: {2,9}.
I'm interested in computing the probability of getting $R$ Raises by rolling $N$ d10, either in a closed form or recursively (I'm thinking of putting this in a script to compute the expected value for some fixed values of $N$).
I'm trying to use this entry on Wolfram MathWorld to solve the problem, but I'm still stuck.
Any help will be appreciated. This is by no means an assignment or a homework or a life-saving problem. I'm doing it just out of curiosity. Thank you very much in advance!
Edit: to clarify, the player should choose the largest number of Raises. For example, if I roll four dice and get 4, 5, 6, 10, although {4, 5, 6, 10} is one Raise, {4, 6} and {10} (or {5, 6} and {10}) are two Raises. In this case the player should choose the second alternative.