According to my knowledge (and wikipedia for example) you confused first and second declension. As for noun "путь", it does not completely follow either declension pattern and normally listed as an exception. Info in this site is correct to my knowledge.
Anyway I am not the site owner and can't modify its content.
I have made some research. Surprizingly there are two contradictory ways of numbering declensions. One of them (presented for example in this site and wikipedia: 1-fem 2-mas) is accepted in school textbooks while another (1-mas, 2-fem) prevails in academic works. That can be annoying indeed.
Thus if you read scientific papers, consider the numbering you insist on. On the other hand absolute majority of Russian native speakers who learned grammar in Russian secondary school (and who you may want to consult with) will number declensions in another way.