A carton of 12 rechargable batteries contains one that is defective. In how many ways can the inspector choose 3 of the batteries and (a) get the one that is defective, (b) not get the one that is defective?

For part "b": you have 1 defective and 11 no defective, so you have a combination 3 by 3 with 11 elements wich are not defective, so 11C2 = 165.

For part "a":you have to choose the only that is defective so you have to order just 2 no defective, i mean from 11 no defective we have 11C2 = 55