Hand Probability Expanded - Is My Thinking Correct

[ligastar]

Fact: The chances of being dealt a "premium hand" A-A, K-K, Q-Q, A-K, A-Q or K-Q preflop in Hold 'Em is 19:1.

Scenario: You are playing Hold 'Em at a full table of 10 players (you are seated with 9 other players).

Question: Is it factual to say that, on average, on every other hand (actually slightly more frequently than every other hand since the chances are 19:1) someone at the table is holding one of these "premium hands"?

Edit: I think I made a mistake above. It would not be slightly more frequently than every other hand @ 19:1 . . . it would be exactly every other hand, on average, at a 10 player table - correct?

Greg H.