A bag contains ten balls, of which four are red and six are blue. An experiment consists of drawing at random and without replacement three balls, one at a time, from the bag.

(a) Draw a tree diagram to show all the possible outcomes of the experiment. Hence, or otherwise, find the probability that

(b) the first two balls drawn will be of different colours,

(c) the third ball will be red,

(d) the third ball will be red, given that the first two balls drawn were both blue. (L)