In the book Ken Warren teaches Texas Holdem, its explained that there are 1,326 possible combinations of hole cards. Then its explained that if you disregard suits, there are 169 possible two-hole cards. Then its explained that 1 of 17 hole cards is a pair. Then its explained that the odds of being dealt any specific pocket pair is 220 to 1. Finally, he says that "if you know nothing of your opponents hand, you can know that odds are 16 to 6 or 8 to 3 that he does not have a pocket pair. The unpaired hand is two and two-thirds more likely than the pair (6 × 2 2/3=16)."
Can someone explain to me this jump in logic? How is it that 16 to 6 odds are that any given opponent does not hold a pocket pair?