I listed all the possible affixes that people would consider useful. Now we'll have mainstat always, that's a given. The trouble comes from the other stats. There are 30 total possible affixes that can roll on an amulet. Out of those, in order to get a truly great amulet, you need all 6 to at least roll one of the useful affixes. The probability of this happening is
(10/30)*(9/30)*(8/30)*(7/30)*(6/30)=about a .1% chance, or 1 in 1000.
The math is obviously wrong.
You said it. It is in fact 10c6 / 30c6 = 0.00035, about 1 in 3000.