Permutations and combinations are essential concepts in combinatorics and are used in many competitive programming problems that involve counting arrangements or selections. A permutation is an arrangement of items, where the order matters, while a combination is a selection of items where the order does not matter. For permutations, you often use factorials (n!) to calculate the number of ways to arrange items. For combinations, you use binomial coefficients, often calculated using the formula C(n, k) = n! / (k! * (n-k)!). It's also common to use modular arithmetic to handle large numbers in these calculations. Knowing how to efficiently compute these values is key to solving many counting problems.