Finite Automata

Question

Total number of DFA possible with 2 states q0 → start and non-final, q1 → final
over Ʃ = {a,b} is
(a) 16                 (b) 32
(c) 48                 (d) 64

Answer 1

On every state it has two inputs , so each input can go to one of the two states. So for every state its arrows (->) have four possible combinations. Similarly on second state it also has four combinations.of arrows emerging from it. So i think its 16.

Answer 2

I think if we have.

N is the number of states

S is the alphabet symbols

Then total dfa possible is (choice for initial state) * (choice for final state) *(choice for transition function)

1*1*(N^(N*S))

2^(2*2)

= 16