Digital Logic.

Assume that you are designing an FSM to keep track of the mood of four students working in the digital design lab. Each students mood is either HAPPY (the circuit works), SAD (the circuit blew up), BUSY (working on the circuit), CLUELESS (confused about the circuit), or ASLEEP (face down on the circuit board). How many states does the FSM have? What is the minimum number of bits necessary to represent these states? Please show your work. Writing a formula only wont get credit. Please justify your answer by explaining it.