I am working on a project that needs to be able to calculate the probability of rolling a given value $k$ given a set of dice, not necessarily all the same size. So for instance, what is the distribution of rolls of a D2 and a D6?
An equivalent question, if this is any easier, is how can you take the mass function of one dice and combine it with the mass function of a second dice to calculate the mass function for the sum of their rolls?
Up to this point I have been using the combinatorics function at the bottom of the probability section of Wikipedia's article on dice, however I cannot see how to generalize this to different sized dice.