I have been working on the problem of probability of poker hands,
I have been able to calculate the probability of each hand except one pair and high card hand.
Here is what I have
P1 P2 X1 X2 X3(here P1 P2 are the same)
13C1 * 4C2 (total counts of one pair)
Now total counts of 3 cards distinct from the pair cards
(12C1 * 4) * (11C1 * 4) * (10C1 * 4) / ??
obviously there is repetition in the second term, How do I remove it?
According to wiki ?? valus is 6, I am not able to understand How to arrive at that value
In case of Triple hand, I did this
(13C1 * 4C3) * (12C1 * 11C1)/2 * 4C1 * 4C1
because in this case each terms is counted twice in case of Two distinct cards.
Can someone please help me out here?