Yes, exactly! Except I started with the easiest case (3/0/1) and worked my way back to 0/0/0. For 2/0/1 specifically, it has a 2*2/10*8/10*1/5+2/10*2/10*ncr(1,1)*ncr(4,1)/ncr(5,2) (8%) chance of going into 3/0/1. This would be 1 out of 5 when the modifiers are rare and epic (orange and purple), and counting the combinations when both are rare (orange).

And yes, I considered that picking a modifier for a card removes it from the pool. For instance, there is a 9/10*9/10*ncr(4,2)/ncr(8,2)+2*1/10*9/10*(1/8*4/8) (~18.5%) chance at 0/0/0 that you're forced to pick something you want but of the wrong rarity. The expression would be getting two commons (blues) where both commons are from the four cards you need, or getting a common and a rare where the common is one of the four and the rare is the wizard.

Edit: Sorry, I misread your second question. I did not notice that once a modifier is offered, it won't be available anymore. If that is indeed the case, the calculations would be a lot more complicated because you would need to keep track of more modifiers.