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  • python itertools does all this out of the box. Commented Apr 21, 2016 at 21:25
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    What do you need this for? It's very likely better to state and then try to solve your original problem. Commented Apr 22, 2016 at 8:27
  • @gnasher729 I'm trying to find an optimal set of groups of letters. I want to take each set and run it through a function to give it a score. I'm trying to find the set that has the 'best score', but I want to do the minimum iterations possible. Commented Apr 23, 2016 at 5:54
  • Do you really need them all? Your calculation is only off by a factor of 24, there will still be 1.1x10^14 partitions meeting your specifications. Commented Apr 23, 2016 at 19:03
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    There are four sets of five. There are 24 ways to order them. You counted every ordering of the same four sets, so that you counted both [abcde], [fghij], [klmno], [pqrst] and [fghij], [abcde], [klmno], [pqrst]. Since the sets are not ordered, I just divided your number by 24. Commented Apr 25, 2016 at 18:21