The favourable thing for (c) to be a major product is conjugation of double bonds and highly acidic nature of hydrogen (resulting in elimination of hydrogen at a higher rate) adjacent to carbonyl group (credit $-$ Rover). According to information I have the above reaction is most probably reversible in nature.
(b) should be major product as per mechanism I have given. So which will be the major (or only) product. You may take high temperature conditions if temperature is required as we are doing elimination reaction.