There are in fact 500 such combinations and it is already a slightly messy task to use a random process to select among them uniformly. ![]() Without the d limit there would be an uncomplicated 10 x 10 x 10 cube of possible combinations, but invoking this d limit cuts this cube at a certain hexagonal face and we are faced with the task of determining which of the 1000 combinations lie inside the volume that is at or behind this hexagonal face and selecting each with equal probability. To take a simple example, let b = 3, c = 9, and d = 13. ![]() The trouble is that for large values of b, c, and d there is an enormous complexity to the space of all successful combinations. ![]() On the other hand based on my experience in writing 'randfixedsum', I think avoiding rejection and at the same time having equal probabilities for each successful set of numbers would be a difficult undertaking.
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