To conduct an experiment, a student must fit three capacitors into a circuit. He has eight to choose from but, unknown to him, two are damaged. He fits three randomly selected capacitors into the circuit. The random variable X is the number of damaged capacitors in the circuit. 

a. Draw up the probability distribution table for X.

b. Calculate Var(X ).

c. The student discovers that exactly one of the capacitors in the circuit is damaged but he does not know which one. He removes one capacitor from the circuit and replaces it with one from the box, both selected at random. Find the probability that the circuit now has at least one damaged capacitor in it.