Two boxes each contain three chocolate bars and four fruit bars. Marie-Claire randomly selects, takes out and eats a bar from one of the boxes. She then puts all of the remaining bars into a bag which she offers to her friend. The friend takes two bars from the bag, both selected at random. Let F be the number of fruit bars that the friend takes.
a) Show that P(F=0)=15/91.
b) Draw up the probability distribution table for F.
c) Hence, find the variance of F.