Balls are thrown one at a time and must land in one of the 6 cells with equal probability. Let Xn be the number of occupied cells after the nth

Balls are thrown one at a time and must land in one of the 6 cells with equal probability. Let Xn be the number of occupied cells after the nth throw. 

a)             What is the state space for Xn?

b)            Give the one-step probability transition matrix for the chain {Xn, n=0, 1, 2, ...}.

c)             What is the probability that exactly 3 cells will be occupied after 4 throws?