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Mark - I think your number 87,990 is correct because 175,980 would be counting the same combination in each direction.
So assuming that 87,990 is the correct number and that each entrant is a voter and a negligible number of others votes in that category, the average voter would have to judge 210 battles for all the combinations to be in a single battle.
I would like to know how many battles actually get fought in a category. I seriously doubt each entrant judges 210 times in a month.
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