Omaha math - chance AA is out

[binions]

Posted this on the O8 board too.

In a 10 handed game, if you don't hold an ace, then there are 1128 possible 2 card holdem combinations left (48*47/2), and 6 AA combinations, so it's 187:1 against a single AA combination, or 187:54 that the group wont have an AA among them (since 9 players * 6 combos = 54). In other words, ~3.5:1 someone has AA when you have KK.

If you have an lone A, then it's 1128:3, or 375:1 or 375:54 that an AA is out. So, ~7:1 that an AKK hand runs into AA.

Have I got the math right?