i finished my diploma and advanced diploma in hospital administration.can i join of rthe MBA correspondce courses?

No.. Eligibility for this course- Other Criteria : Any Degree of three years of study duration and a pass in the entrance test conducted by Anna University. Minimum Qualification : Graduate

for MBA you need to have graduation degree with 50% marks from any recoganized university

complete graduation first than try or admission in MBA .as per your information you are not graduate if you are graduate than you may apply. your question not clear this aspects.

For Distance Education you can go for, NMIMS, Symbiosis, ICFAI, Welingkars, these are some of the best institute for distance education.