I want to find the odds of something:

I have 60 objects, of which I am going to select seven. Of these objects, 15 are the same (call them broken). What are the odds of me having at least three broken objects in my selection of seven?

I intended to go about this along the lines of

Second question:

Say 15 are broken in one way (A) and 7 are broken in another way (B). I now select ten of them. What are the odds of having at least two broken in one way and three broken in the other?

Do I multiply these odds (assuming I'm setting the problems up correctly in the first place) just like I would simpler probabilities? At this point i'm assuming that none of the objects are broken in both ways at the same time.

Thanks. Also, I've looked for sites dealing with the second question online and found little to nothing. Any sites you can direct me to so I can find my own answers. Not that I don't like giving you something to do. . .