I'll start off by admitting that this is a HW problem. However, my main goal is to find out what kind of problem this is classified as and what concepts I need to learn to be able to solve similar ones. I'm not just looking for an answer (although I would be glad to get one); I need help by being pointed in the right direction. Links to relevant articles and readings would be appreciated.
A shipment of 12 X-Ray machines includes 4 that are defective. In how many ways can a hospital purchase 5 of these machines and receive at least 2 of the defective machines?
I can only get as far as figuring out that there are 792 different ways to purchase 5 machines from the shipment of 12 (12 choose 5 is 792).
I realize this might be very easy for some people, but all I need is a little help (links and explanations is what I'm after, not just an answer). Thanks in advance!