Hi, I don't know how to prove that it is a Markov Chain

Roll a fair die repeatedly and let Y1, Y2, . . . be the resulting numbers. Let Xn be the number of different outcomes we have seen in the rst 71 rolls for n 2 1, that is, Xn = #{1/1,Y2, . . . ,Yn}, and set X0 : 0. (1) Show that X\" is a Markov chain and nd the transition matrix. (ii) Let T : min{n : Xn : 6} is the number of trials we need to see all 6 possible outcomes at least once. Find E[T]