Count the Number of Dfa's

Question

How many DFA's can be constructed with 3 states and 2 input symbols which accept empty language?

Comments

1098 Dfa

Answer 1

States	a	b
q1	3	3
q2	3	3
q3	3	3

=3^6 =729

now, there is 2^3 combination in which final state can be chosen.

and initial state can be any of three i.e 3 ways to select initial state.

total=729 * 2^3  * 3 = 17496 dfa's

In general, when

n = no. of states

m= no. of input alphabets

total no. of dfa's = n^mn * 2^n * n

Comments

This solution is wrong...

U are giving the total number of DFA's possible with 3 states and 2 input symbols but the question is asking about  DFA which accept empty language. So u should have removed some cases like the initial state will never have final state otherwise it will accept the empty string which will not be the solution.