This DFA will accept all strings of length n (n ≥ 3) which has minimum of 2 consecutive 1's in
last (n-1) positions
no.of possibilities in first position=2
no.of acceptable strings with 6 positions = (total possible strings – no.of rejected strings)
total possible strings =2^6 =64
no.of rejected strings
string which contain only 0’s=1
strings which contain only one 1 = 6 (_0_0_0_0_0_)→ we can place 1 anywhere.==> 6c1
strings which contain two 1’s but not consecutively = 10 (_0_0_0_0_)→ 5c2
strings which contain three 1’s but not consecutively= 4 (_0_0_0_)→ 4c3
now total no.of rejected strings = 1+6+10+4=21
no.of accepted strings of length 7 = 2*(64-21) = 2*43 =86
so the answer is 86 strings