Which of the following statements are correct ?

Which of the following statements are correct ?
(1)    For a finite state Markov chain there is at least one transient state.
(2)    For a finite state Markov chain there is at least one stationary distribution
(3)    For a countable state Markov chain, every state can be transient
(4)    For an aperiodic countable state Markov chain there is at least one stationary distribution.