Find the number of strings in finite automata:

Question

Given finite automate accepts strings of length 6.

How many strings are there in the set?

a. 18

b. 20

c. 30

d. 32

Answer 1

To reach final state we have to move 3 times up and 3 times right.

So total possible way to reach final state = $\frac{6!}{3!*3!}$ =20

Hence,Option(B)20 is the correct choice.

Comments

here

Number of ways  to reach final state = Number of string accept by the given Dfa.

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Thats nice. So, the characters in the edges matter :)

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yes Sir

Answer 2

My answer is 24. 

0 state--> 1 state : 2 ways

1 state --> 2 state: 4 ways

2 state -> 3 state: 6 ways

3 state -> 4 state : 6 ways

4 state -> 5 state : 4 ways

5 state -> 6 state: 2 ways

Total Number of transitions: 2 + 4 + 6 + 6 + 4 + 2 = 24 WAYS

Please correct if I am wrong!