So I wanted to follow up on question I asked yesterday (that was well answered), but I wanted to look at it in a more visual way.
I was asking how many ways there are to make a full house in Poker without using the combinations method. I was well explained the formula :
\begin{equation}\frac{52\times3\times2\times48\times3}{3!2!}=3744\end{equation}
But now if I try to explore the different ways with a diagram such as the one below, would there be a way to make a calculation out of it?
My reasoning could be wrong, but I believe we could start by picking any card (let's call it A), followed by any other (which will be A or a different one B). If that second card is A, I could still choose any of the 50 remaining cards (looking for a third A or any new value). However if that second card is B, the possibilities now drop to 6 because I could then only choose one of the three remaining A or B.
I don't know if my diagram is right or makes sense, but with a similar approach is it possible to make a calculation to obtain the answer 3744?
