MODULE 2 - FACTORIAL

Factorial

is a fundamental mathematical operation that plays a crucial role in counting, combinatorics, and probability. It is the basis for determining the number of possible arrangements or selections in a given set of objects

Christian Kramp

The factorial notation, 𝑛!, was introduced by the French mathematician ___ in 1808.

Louis Francois Antoine Arbogast

The term “factorial” was first coined in French by____ in 1800

Exclamation Point

Kramp adopted Arbogast’s term and created ___ for printing convenience, a symbol that is now universally used. He introduced it in his work, Elemens d’arithmetique universelle.

Recursive Property

Factorials can be defined recursively as 𝑛! = 𝑛 × (𝑛 − 1)!, for 𝑛 ≥ 1, with the base case 0! = 1(Grimaldi, 2004)

Growth Rate

Factorials grow extremely fast as 𝑛increases. For instance, 10! = 3,628,800. This rapid growth makes factorials useful in analyzing computational complexity (Rosen, 2019).

Relation to Permutations and Combinations

Factorials are essential in computing permutations (𝑃(𝑛, 𝑟) = 𝑛! (𝑛−𝑟)! ) and combinations (𝐶(𝑛, 𝑟) = 𝑛! 𝑟!(𝑛−𝑟)! ), which are core concepts in combinatorics (Epp, 2011).