(10 points) A certain computer science department consists of 10 tenured or tenure track faculty. Suppose 3 faculty members are to be randomly selected to collaborate on writing a new course that will be added to the computer science program. (a) How many different ways can we select the faculty that write this new course? (2 points) (b) If the faculty are ranked 1, 2, ... , 10 in order of their teaching ability, how many dif- ferent ways to choose the faculty that write the course would include the best teacher? (2 points) (c) What is the probability that the chosen faculty members contains at least 1 of the 5 best teachers? (3 points) (d) What is the probability that the chosen faculty includes neither of the two best teach- ers? (3 points)