Factorial
The factorial of a positive integer is the product of all positive integers smaller than and equal to that number.
Explanation
A factorial indicates in how many ways you can arrange n elements
It is called n-factorial.
Example 1
We will play with the letters ABCD. Successively we pick more and more letters and see how many variations we can make with them. With 1 letter you only have 1! = 1 possibility
A
With 2 letters you have 2! = 1 × 2 posibilities
AB BA
With 3 letters you have 3! = 1 × 2 × 3 = 6 possibilities
ABC BCA BAC
ACB CAB CBA
With 4 letters you already have 4! = 1 × 2 × 3 × 4 = 24 possibilities
ABCD BACD CABD DABC
ABDC BADC CADB DACB
ACBD BCAD CBAD DBAC
ACDB BCDA CBDA DBCA
ADAB BDAC CDAB DCAB
ADBA BDCA CDBA DCBA
That increases fast. We have seen above that
You can decide not to take any letters. That is also a possibility. So by definition zero-factorial is
HistoryThe French mathematician Christian Kramp (1760 - 1826) invented the symbol n! for the factorial. |