[ QUOTE ]
Chance of being dealt any A23x hand (x not an ace)
c(4,1)* c(4,1) * c(4,1) *c(46,1)/c(52,4)=0.010875
[/ QUOTE ]Frank - Not quite. You have some duplications here too.
There are generally a number of ways to approach this problem.
One way is to make a chart. Here would be my chart:<ul type="square">AA23
A223
A233
A23X (where X is neither an ace, a deuce, or a trey).
then
AA23...6*4*4 ways to do this.
A223...4*6*4 ways to do this.
A233...4*4*6 ways to do this.
A23X...4*4*4*40 ways to do this.[/list]Then multiply as indicated and add the four sub totals.
96+96+96+2560 = 2848.
Then it's 2848/C(52,4) = 2848/270725.
And that's the probability. Divide to convert from a fraction to what I'd call a decimal fraction. (0.01052)
In this case, I'm going to call it about 1% anyway. But your fundamental approach is wrong.
I advise you to make a chart such as the one I made if you want to make your probability calculations more correct. Basically I mentally separated the aces, deuces and treys from the rest of the deck. (I don't know if that makes sense to you or not).
I'll leave it to you to correct the remaining ones, if you choose to do so. That's a better way for you to learn than my showing you how to do each one.
Buzz