What are the chances/odds of obtaining one?

Question

What are the odds of obtaining one of the best following starting hands in Omaha Hi Poker?

AAKK double suited

AAKQ double suited

AAJT double suited

AAPP where P is another pair, double suited.

And what would the combined odds be?

Answer 1

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P( As Ah Ks Kh ) = 1/52 * 1/51 * 1/50 * 1/49 as is every combination of definite cards (1/6497400)

Multiply this by 24 since it doesn't matter what order they are dealt

and Multiply it by 6 since it doesn't matter what combination of suits you receive.

Answer = 144 chances in 6497400 = 0.0022%

By the same formula, assume you want exactly As Ah Ks Qh

multiply by 24

multiply by 12 as you now have double the chance since AKs AQh is different to AQs AKh

Answer = 288 possibilities, 0.0044%

AAJT is exactly the same 0.0044%

AAPP double suited now has 11 times as many combinations as AAKK

Answer = 0.0244%

SInce the hands are independent possbilities the odds can simply be added.