The old "Four numbers equal 24" problem

Any time I see a question like this: http://www.mathhelpforum.com/math-he...make-24-a.html I wonder:

Of the possibilities of digits, how many can be solved by the four simple operations, how many can be solved if we allow other symbols, and how many are unsolvable?

I can't come up with any way to google an answer, though I'm sure someone must have done this before. Any interest?

I'm confident that (1, 1, 1, 1) cannot be made into 24, regardless of operations.

Anyone want to join in to help with the other 6560 possibilities?