It's past my bed-time and there's a whopping 5 points at stake, so I'm going to violate my own #1 Prime Cardinal Rule here, and just give a stripped down answer without going through a full explanation.
The number of combinations of 3 cows out of 7 is (7·6·5) / 3! = 35 .
The number of combinations of 2 pigs out of 4 is (4·3)/2 = 6
The number of combinations of 10 sheep out of 10 is 1 .
The number of ways he can select his animals is (35 · 6 · 1) = 210 .
