Use order counts instead of expanding every draw path

A box contains 5 white balls,3 red balls and 2 green balls.

(i) Three balls are taken at random with replacement. Find the probability that they all have different colours.

(ii) Five balls are taken at random without replacement. Find the probability that (a) exactly 2 are white, (b) at least 2 are white, (c) exactly 2 are red, given that at least 2 are white.