Find the order of these True-False questions.?

Here's the question:


A science quiz consists of five true-false questions.


There are more true than false.


Questions 1 and 5 have opposite answers.


No three consecutive answers are the same.


Josh knows the correct answer to the second question.


From this information, Josh can determine the correct answer to each question.


What are the correct answers to each of the five questions on the quiz.Find the order of these True-False questions.?
If Q1=T


Q5=F





T???F


There needs to be at least 3 T's, so the remaining 3 must have 2 T's and an F, and can't all be T's because then there'd be 3 in a row


TTTFF - No, 3 T's in a row


TTFTF - Ok


TFTTF - Ok








If Q1 = F


Q5 = T


Similarly, possibilites are:


FTTFT - Ok


FTFTT - Ok


FFTTT - No, 3 T's in a row





So the possibilities are:


TTFTF


TFTTF


FTTFT


FTFTT





So if knowing the answer to Q2 leaves only one possibility, he must know Q2 = F, leaving:





TFTTF