[*TT*]

Thanks Bruce, your right there is only one A unaccounted for, I must have made an typo when I tallied up the cards which I carried over here.

so using combinations I have learned that the villain pairs the board 56% of the time assuming he holds any 3-card bike. If we remove the roughest bike hand of (45)2 from his capping range to more accurately represent his likely holdings if he is slightly loose then there is a 39% chance he paired. In the event we open the villain's range to include all but the roughest sixes then there is a 28% chance the villain paired the 5.

thanks a bunch for your help!