There are nine different books on a shelf; four are red and five are green. In how many different orders is it possible to arrange the books on the shelf if

a. there are no restrictions;

b. the red books must be together and the green books together;

c. the red books must be together while the green books may be, but need not be, together;

d. the colors must alternate, i.e. no two books of the same color may be adjacent?