How many 5-card hands contain two of one rank and three of another rank? What is the probability of being dealt such a hand?
I am not actually taking any classes that cover probability at the moment, so I don't have a lot of background knowledge for this one. I am, however, covering inclusion/exclusion at the moment so I gave it a shot.
There are 13 ranks and I need to choose 2:
Once this has been done, I need to choose 2 from one rank:
and 3 from the other rank:
So there are:
My answer is different from the one provided, I'm not sure why...
How do I calculate the probability of being dealt such a hand once I know how many possibilities there are? Is it just ?