Bad post. I think most people acquainted with combinatorics would prefer the linearity of expectation explanation going more like: (n choose m)*(m-1)/m*(m-2)/m*...*1/m where the (n choose m) counts the number of m-tuples and the other part is the probability a particular m-tuple has distinct values thus being counted precisely once in the product of multiplicities. It is a classic double counting argument.
so for the original question of a regular d3 then yeah admittedly what you said is a lot cleaner and a better approach. maybe i'm just coping, but i think that what i wrote is still fine because it can be used for non uniform probabilities of a dk and therefor generalizes better (not cope?). i will go back and use this logic to improve it though (:
Bad post. I think most people acquainted with combinatorics would prefer the linearity of expectation explanation going more like: (n choose m)*(m-1)/m*(m-2)/m*...*1/m where the (n choose m) counts the number of m-tuples and the other part is the probability a particular m-tuple has distinct values thus being counted precisely once in the product of multiplicities. It is a classic double counting argument.
OK dog, I will try to be friendlier in future criticism.
so for the original question of a regular d3 then yeah admittedly what you said is a lot cleaner and a better approach. maybe i'm just coping, but i think that what i wrote is still fine because it can be used for non uniform probabilities of a dk and therefor generalizes better (not cope?). i will go back and use this logic to improve it though (: