From what I understand, the question is asking me to find P(X(t) = n | X(0) = N). I know that with a linear death rate this probability is (N choose n) * [e^(-alpha*t)]^n * [1 - e^(-alpha*t)]^N-n but I don't think this is true for a constant death rate. Any help on how to approach this would be great! Also, I see in the final solution that there are two answers: one for n = 1, 2, ... N and another one for n = 0. Why is this case? And how would I go about finding both cases? Thanks!