Ann, Barry and Clare are three students taking a multiple choice examination paper. For each question a student has to select the correct answer from five that are offered. For Question 1, Ann has no idea of the correct answer, Barry correctly identifies one answer that is wrong and Clare correctly identifies two wrong answers. All three students decide to guess at random from the answers they think stand a chance of being correct. Calculate the probability that

(a) none of the three students chooses the correct answer,

(b) Clare is the only one to choose the correct answer,

(c) exactly one of the three students chooses the correct answer. (NEAB)