The positions of nine trees which are to be planted along the sides of a road, five on the north side and four on the south side, are shown in the figure.

(a) Find the number of ways in which this can be done if the trees are all of different species.

(b) If the trees in

(a) are planted at random, find the probability that two particular trees are next to each other on the same side of the road.

(c) If there are three cupressus, four prunus and two magnolias, find the number of different ways in which these could be planted assuming that trees of the same species are identical.

(d) If the trees in

(c) are planted at random, find the probability that the two magnolias are on the opposite sides of the road. (L. Additional)