In the fourth sequence of the Hidden Gems seminar series, we are going to discuss the Karlin-McGregor theorem which computes non-coincidence probability, i.e., the probability of non-collision, for strong Markov processes as the determinant of a certain matrix obtained from the transition probabilities. The theorem has been widely used in many fields. In combinatorics it counts nonintersecting lattice paths, n-candidate ballot problem, and monotone dominance ordering. More recent applications include statistical mechanics, random matrix theory, determinantal point processes, and queueing theory. We will talk about the history and generalizations of the main result and touch on some of its applications. Part of the material is taken from a paper by W. Bohm and S. G. Mohanty (1997).