Don't fret- litterbox training IS possible!
10 months IS old for a pup to have some bad habits, but my Oliver is 100% little box trained. He's 6 months old right now and has been solidly trained for three months (a week of him testing his limits and pooping on the stairs...) but aside for that he's perfect about goin gin his litterbox.
The great thing about him is that he does both. On walks he'll go outside (or if we're in the yard playing all day) and when we're inside he knows where his litterbox is.
I don't think it's impossible, at all, to expect a pup to be litterbox trained. Some people are surprised, but it makes my life 100% easier. I go to school for part of the day and I live with roommates who can't always be home so Oliver needed somewhere to go when we weren't around. It just makes sense.
Anyways... THe only thing I can say is that consistant training pays off. I was 100% consistant for the first couple of weeks with Oliver. Everytime he was out running the house I ran upstairs with him every 15 minutes or so to show him where his litterbox was and told him to "go potty". THen it's the old routine praise praise praise treat.
A lot of people say their yorkies are never 100% trained... but they really are like all other dogs- they just need consistant training. I'm proud of my boy, but I know it could have easily turned out TROUBLE if I hadn't been ontop of it. Oh i can't image the wreckage! hehe
I wish you luck! If you have any questions feel free to PM me.