There are n! ways of arranging n distinct objects into an ordered sequence.

That would only be true if the OP allowed duplicates; Ie. if a set consisting of 80 x bit 0 was allowed, but the OP does state:

How would you quickly iterate over every combination of an array with 80 elements where each element is used a maximum of once in the combination?

Thus the maximium number of sets is 2^80.

He also made no mention of "ordered".

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In reply to Re^3: Turning very larger numbers into an array of bits by BrowserUk
in thread Turning very larger numbers into an array of bits by gblack

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