In 1654 Fermat and Pascal exchanged letters about how to divide the stakes of an interrupted game of chance. Fermat's approach was purely combinatorial: enumerate every possible future sequence of plays, count the ones favourable to each player, and divide accordingly. This was the first rigorous treatment of probability as a ratio of countable outcomes.
Fermat demonstrated that complex uncertain situations could be decomposed into finite sets of equally likely outcomes. By counting systematically rather than relying on intuition, he transformed gambling questions into precise mathematical problems. This combinatorial framework remains the foundation of discrete probability.
The principle that uncertain outcomes can be exhaustively enumerated and their probabilities computed exactly is the basis of option pricing, scenario analysis, and Monte Carlo simulation. Every time a quantitative system evaluates the probability of a corporate event, it is applying Fermat's combinatorial logic.
Combinatorial enumeration is how we evaluate the probability space of corporate events — M&A outcomes, earnings scenarios, regulatory decisions. Fermat's insight that you can count your way to a probability is the first principle of quantitative finance.