Have you created @Test Annotation inside it

It should be present in order for the test to be executed.

Yes Ashish I have the @Test annotation and I have spent time on google/stackoverflow to try figure this out. 

I even made a new project from scratch out of frustration and installed a new Eclipse. I have been stuck for a few days now due to some minor issue that needs resolving. 

If I create a main method in the test classes it does show me the option to run it as "java application". without it I see no option.

I have TestNG and selenium files downloaded through Maven dependencies. 

Solved. 

Solution: install TesNG plugin for Eclipse from the Marketplace