Integrate Facebook likes with wordpress site and order it.

Hey. New to the forum.

I got a customer asking for a simple blog. Ok, easy so far.
Under each blogpost he’d like a “Like”-button that’s integrated with Facebook. Ok, easy so far (Found plugins and guides).

But in the sidebar he wants a top ten toplist. These are supposed to rank after the Facebook likes.

My question: Is this even possible or do I have to explain to him that I
can’t do this? Or tell him he’d probably have to have another solution that’s not Facebook-connected?

Thanks for any help!