What we know:
Its a DFA hence for each symbol in the alphabet goes to a single state.
There will be a single start state and multiple final states.
4 states on both the symbols of alphabet can go to one of the four states, statesstates*symbols=44*2
We know that the initial state is known.
Any of the four states can be final state, hence 24
So in total 24*44*2=24.22*4*2=220
We are said 2n number of DFAs and asked value of n. So, the value of n is 20. :-)
If you didnt understand the see the following
Consider the following transition table
|
a |
b |
--->W |
W or X or Y or Z |
W or X or Y or Z |
X |
W or X or Y or Z |
W or X or Y or Z |
Y |
W or X or Y or Z |
W or X or Y or Z |
Z |
W or X or Y or Z |
W or X or Y or Z |
We are said that there is a designated Start state lets say the designated start state is "W"(if that was not said then we would have multiplied by 4)
There are |states| * |symbols| cells and each may have one of the 4 states, this is how we get 44*2
And a state can be final or non final hence we multiply it by 24.