## Definition ==Combinatorics== is the branch of mathematics concerned with counting, arranging, and selecting objects from finite sets. In probability, combinatorial methods are used to count the number of favorable outcomes and the total number of outcomes in order to compute probabilities in equally likely sample spaces. > [!example]- How many distinct ways can 5 people be seated in a row of 5 chairs? > Each arrangement is a permutation of 5 distinct people. The first chair has 5 choices, the second has 4, and so on. > $ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 $