Your solution for A isn't correct because it's asking specifically for grabbing only one defective. Your solution allows for grabbing both defectives as well. To answer this you could reason that you need to grab only one defective so there are 2c1 ways to do that. Then you need to grab two non defectives so there are 10c2 ways to do that. Multiply them and you get the solution.
For part B you know you need both batteries and there are 2c2 = 1 ways to get both and then you need to select one of the non defectives and there are 10c1=10 ways to do that. Multiply together and you have your solution.