A drawer contains 5 pairs of green socks, 3 pairs of black socks, and 4 pairs of red socks. The 12 pairs of socks are jumbled together in one drawer, but each sock is still attached to its mate. You reach into the drawer and pull out 3 pairs of socks, one at a time, without putting any back. What is the expected number of pairs of green socks? Provide evidence of your work by typing out your full solution.