Normalise the maximum score and count three-round orderings

An unbiased six-sided die is rolled twice. X is the higher value when they differ, or their common value when equal. Its distribution is $P(X=r)=k(2r-1)$ for r=1,2,3,4,5,6.

(i) Find the exact value of k as a fraction in simplest form.2 marks

(ii) Find $E(X)$.2 marks

One round consists of two rolls, with X as the score. A player plays three rounds.

(iii) Find the probability that the total score is 16.2 marks