It’s not really important, all that matters is that we’re consistent in which one we use. We have to always include the symmetry factor, or never include it.
In this case, I went with counts because our data does, in fact, consist of counts. Because we’re assuming each die roll is independent, we’d get the same answer if we just made up a string of outcomes with the same counts, and used that as the data instead.
It’s not really important, all that matters is that we’re consistent in which one we use. We have to always include the symmetry factor, or never include it.
In this case, I went with counts because our data does, in fact, consist of counts. Because we’re assuming each die roll is independent, we’d get the same answer if we just made up a string of outcomes with the same counts, and used that as the data instead.