Definition, Meaning & Synonyms
subfactorial
noun
/sʌbˈfæktəˌriəl/
Definition
The subfactorial of a number is a mathematical term used to represent the number of ways to arrange a set of objects such that no object appears in its original position.
Examples
- For example, the subfactorial of 3, denoted as !3, equals 2, which means there are 2 ways to arrange 3 objects so that none of them is in their original position.
- In a party task where you want to assign 4 people to 4 different rooms without anyone ending up in their own room, you would calculate the subfactorial of 4: !4 = 9.
Meaning
Subfactorial is often denoted as !n or D(n), where n is the number of objects. It is particularly relevant in combinatorics and probability theory.
Synonyms
- derangement
- permutation without fixed points
