I have two CSS classes on one HTML element: .c-headline-1 and .c-hero__headline. In my external style sheet, I'm using .c-headline-1 and in an internal style sheet (<style type="text/css">) I'm using .hero__headline, but for some reason the .c-headline-1 property values are overwriting some of .hero__headline's property values. For example, if both have a font size declaration,  .c-headline-1 is behaving as if it has higher specificity since it's overwriting .c-hero__headline's font size.
I thought internal style sheets had higher specificity than external style sheets or no?