I didn't consider trips. I misinterpreted your question as asking for 2-pair not caring if you got a boat or quads. You also have to multiply my quad calculation by 6.


Your method counts some combinations twice. The problem comes in when you multiply by 3. For example, look at 8s 3s 3c and 3s 3c 8s. When you multiply by 3, the second combination generates the first one.


Here is the correct solution breaking it into 4 cases:


hole cards: 83o


2-PAIR (83x or 38x *3, x not 8 or 3):


(6/50)(3/49)(44/48)*3 = 2.02%


TRIPS (88x or 33x *3, x not 8 or 3):


(6/50)(2/49)(44/48)*3 = 1.35%


BOAT (838 or 833 *3):


(3/50)(3/49)(4/48)*3 = .091%


QUADS (888 or 333 *3):


(2/50)(1/49)(1/48)*6 = .01%


TOTAL: 3.47%