You start with five dice. Roll all the dice and put aside those dice that come up 6. Then, roll the remaining dice, putting aside those dice that come up 6. And so on. Let Xn be the number of dice that are sixes after n rolls.

(a) Describe the transition matrix P for this Markov chain.

(b) Find the probability of getting all sixes by the third play.

(c) What do you expect P100 to look like? Use R to simulate to confirm your answer.