Sometimes combinatorial experiments are faster and more successful than computational methods.
And sometimes not.
Correct me if I am wrong, but combinatorics only works in a discrete space setting?
Can you find the Black Scholes price using combinatorics?
Agreed!
Computational models (whether they use discrete or continuum variables) can only beat trail-and-error experiments if the models are sufficiently accurate. In the case of high temperature superconductors, no one had a clue on how to compute which alloys of which elements would superconduct at which exact temperatures. They may have had some theoretical hints that superconductivity might occur in these complex alloys but no way to compute exactly which ones would do what.
As for Black Scholes using combinatorics, what about using binomial trees and Pascal's triangle to compute the price?
A related issue occurs with the Mandelbrot set in which the fastest way to judge membership in the set is to numerically iterate until a stopping condition occurs (which may take near-infinite time) because there's no analytic solution for the set boundary.
Exactly which physical/empirical, numerical/computational, or analytic/logical operations arrive at an accurate answer with the least resources varies significantly across the set of all possible questions.