[gaming_mouse]

[ QUOTE ]
1. I was wondering how Mike Caro arrives at 2592 combinations to Aces-up in 5draw (no joker) when drawing 3 to 2 aces?

I tried to figure it like this:

pair combinations (3 ranks with 3 cards): 3 * C(3,2) * 45 = 3 * 3 * 45 = 405
pair combinations (9 ranks with 4 cards): 9 * C(4,2)* 45 = 9 * 6 * 45 = 2430

for a total of 2835 two pair combinations

What am I doing wrong?

[/ QUOTE ]

I don't follow what you are doing. But I get:

12 non-ace ranks, each with 6 (4 choose 2) possible pairs. Each of those pairs can have any of 44 possible kickers. Thus:

12*6*44 = 3186

which does not agree with either answer. Am I misunderstanding the question? I am counting the number of 3-card draws you can pull which, along with the aces you already hold, will give you 2 pair.


[ QUOTE ]
2. I tried to figure how Mike Caro arrives at 1854 combinations to 3-Aces in 5draw (no joker) when drawing 3 to 2 aces?

[/ QUOTE ]

2*( (48 choose 2) - 12*6) = 2112