Personally I would discuss Graph theory, in a diverse and conceptual way with a few deeper dives. Students of that level should be familiar of weighted graphs, have an intuition for the size of functions (which could be leveraged in a discussion of travelling salesman, big O notation, how quickly networks can grow, Ramsey Theory R(3,3), chromatic polynomials, etc). There is so much novelty in graph theory, and it draws many areas of maths together in novel ways.
At a minimum, I'd include Erdös Renyi Random Graph models, and the emergance of a large connected cluster. It is an accessible mention of asymptoic analysis, simple graph enumeration, and probability distributions(as the edges per node modelled via Poisson is appreciably different to edges as randomly selected pairs of nodes).
Depends on time and how quickly you move through content, but you could try to mention dynamical systems, such as predator-prey models, and how graph theory can be applied in the spread of diseases and informtion.
I think this topic is well suited, because it is an example of three important chracteristics of matha: Interconnected, Rich in application, and the sheer enormity of open problems. E.g. P=NP, Graph Homomorphism, Ramsey (5,5,), etc.
At 2nd year ans above, it is likely many already have heard of Monty Hall,C
Cardinal Infinities, and Mandelbrot(although this could be included if you hedge your bet with a split between dynamical systems and graph theorg).