Learn this formulation:
div.classname p {blahblah}
or even
body.classname p {blahblah}
This means: any paragraph
inside a div with the given name has the named set of attributes. You probably want to go with div rather than body, unless you can be certain you'll never have paragraphs for things like shared navigation that presumably won't be red and green.
:: insert boilerplate about how you should call the div something other than "green" because what if next year you decide to change the color scheme* ::
You can then override it with
div.classname p.newclass {blahblah}
where you only need to specify the "div" part if the css for p.newclass includes elements that are
different from the generic p-within-the-div, like
div.classname p.black {color: black;}
You can also do things like
div.classname > p
meaning "this rule only applies if the p is directly inside div.classname, not if it's inside some intermediate element":
div.green > p {color: green;}
div.black > {color: black;}
You can now nest div.black and div.green inside each other.
* Sure, there are exceptions. I've got one directory that's made up entirely of "body class = 'pink'" "body class = 'blue'" "body class = 'tundra'" and so on, because each page's color scheme is determined by its preset content.