The factorial operator calculates the product of all positive integers up to a given number. For example, the factorial of the number is calculated like this.
In its simplest form, the factorial operator is used for counting and arranging items. For example, the number of unique ways to arrange the set is equal to . The possible arrangements of this set, called permutations, are shown below.
- (🍄, 🌿, 🐟)
- (🍄, 🐟, 🌿)
- (🌿, 🍄, 🐟)
- (🌿, 🐟, 🍄)
- (🐟, 🍄, 🌿)
- (🐟, 🌿, 🍄)
The factorial operator also appears in many other areas of mathematics, such as probability and statistics in distributions like the binomial distribution, poisson distribution, and multinomial distribution. In calculus, it is used in series and sequences, and taylor series.
Shown below are some basic examples of the factorial operator.
The factorial operator is used in the formulas for permutations and combinations.
The number of permutations of n distinct items is given by n factorial. A permutation is a unique ordering or arrangement of the set of items.
The combination formula calculates the possible combinations of r elements out of a group of n elements where order does not matter.
The permutation formula calculates the possible permutations of r elements out of a group of n elements where order does matter.
Multiplication is a basic arithmetic operation performed on two numbers. Multiplying a number by another number is the same as taking n groups of the other number.