Use factorials, binomial coefficients, and modular arithmetic to handle large numbers.

Combinatorics problems often involve counting arrangements, selections, or combinations of elements. Factorials and binomial coefficients are the core concepts used to solve these problems. The number of ways to arrange n items is given by n! (n factorial), while combinations (selections without regard to order) are given by the binomial coefficient formula C(n, k) = n! / (k! * (n-k)!). For large inputs, modular arithmetic is essential to avoid overflow, especially when working with large factorials. Precomputing factorials and using modular inverses can significantly speed up combinatorics calculations in competitive programming.