Question: A week before the final exam, Professor Gottesman gives his students ten questions. At the beginning of the final examination, a student will reach into a wastebasket and blindly select three of these ten questions, which then become the final exam. You are well prepared to answer six of the ten questions and poorly prepared to answer the other four.

a) What is the probability that the three selected questions will all be ones that you are well prepared to answer?

b) What is the probability that the three selected questions will include two that you are well prepared for and one that you are poorly prepared for?

c) What is the probability that the three selected questions will all be ones that you are poorly prepared to answer?