Construction of FA's -number of FA's

Question

Number of FA's possible for two states X,Y over the input alphabet {a,b} where X is always the initial state and the FA should accept only empty  language ?

Comments

please Before adding the question, just check is it asked or not?

duplicate of https://gateoverflow.in/16808/many-state-drawn-over-alphabet-which-accepts-empty-language

Answer 1

here we will have 2 cases :

CASE 1 : when we donot have any final state means each symbol can goto any state means each symbol has 2 choices for any state.

CASE 2 : when we have 1 final state but its not reachable. so final state will have 2 choices of states to move on to for each symbol and initial will have only one choice.. so ^{answer is 20} as initial state is fixed.