[pococurante]

And getting back to the original question. I assume that 59280 is the correct number.

So let's say I give you a random 5 card hand that is one of those 59280 possible combinations. I then ask you to set the three of a kind off to the side. You now have 2 random cards out of the 49 possible cards you could have had.

Flip over random card #1. What are the odds that it is one rank above or one rank below your 3 of a kind... it should be 8/49, correct?

But 8/49 * 59280 equals 966.5. How is it possible for there to be 966.5 poker hands that qualify? There is no such thing as half of a hand. This makes no sense.