Markov Chain (transition matrix)

Hey guys can anyone help me obtain the transition of the markov chain with states being the number of projects the architect has in hand at the beginning of a month.

[ Quote:

An architect can handle up to 3 projects at once. During any month there is a

probability of 0.5 of acquiring one new project (to start the next month) provided the architect knows that the project can be handled, otherwise no new projects are

acquired. That is, the architect decides to take the honourable course of not taking on a new project for the next month unless it is known that it can be handled. Existing projects are equally-likely to finish by the start of the next month or to continue, independently of each other.

Thank you