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I've a problem. Let's say I have 18 independant events. The outcome of each event could be 0, 1 or 2, with a probability of 0.5, 0.333 & 0.167, respectively. I want to know the easiest way to calculate the probability of achieving all scores between 0 & 36. As there's more than a 0 or 1 (or yes/no) answer I can't use the binomial distribution. Any help would be greatly appreciated.

Regards

Andrew