**Combinatorics** is the branch of mathematics that studies the enumeration, arrangement, and structural relations of finite discrete objects. In probability, combinatorial methods are used to count the number of favorable outcomes and the total number of outcomes in order to compute probabilities. --- > [!example]- Combinations of people in chairs > How many distinct ways can 5 people be seated in a row of 5 chairs? > >[!answer]- > > 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 $