(i) A box contains balls of three different colours: red, green, blue. There are an equal number of balls of each colour, and balls of the same colour are identical. If denotes the total number of ways of selecting balls from the box, show that is divisible by 6.

(ii) As previously, but now let be the total number of ways of selecting balls such that there is at least one ball of each colour. Prove that is divisible by 3.