Yes, you can surely apply for admission in BA LLB course if you are an arts stream student. Admission in top colleges is based on merit through entrance exam. You can apply for CLAT which is the best option for you.
Lawyers are in great demand in every organisation. Most of the companies hire lawyers for legal issues and if you are a good lawyers then you will definitely make a great career.
Please restructure your question. Do mention the name of university you wish to pursue your BBA LLB degree so that I can clarify your doubt.