[BruceZ]

Is this problem so hard that no one knows the answer?
Or....so elementary I should have never asked?

Actually both. To anyone who knows how to do it, it is too elementary to be interesting while at the same time being too tedious to want to spend time on. I have made recent posts on how to calculate the odds of making both straights and flushes, so you should be able to use these same methods for combined straights and flushes with various numbers of outs. If you run into trouble and have specific questions about how to proceed, I'm sure I and others could answer them. I may do this problem at some point myself, since the answer could be useful.