In this talk, we explain three counting problems related to finite fields, which are derived from algebraic combinatorics, discrete geometry, and number theory. First, we introduce an interesting counting formula related to $q$-binomial coefficients and see counting combinatorial objects is interesting itself. Second, we discuss the incidence problem and see how spectral graph theory is helpful to study it. Lastly, we describe the topic of Diophantine tuples and see how combinatorics helps to solve the related problems.