Learning Objective:
What is Factorial?
What is n x (n - 1)!
Concept:
The product of 'n' natural numbers is called factorial.
For example if we multiply first 5 natural numbers, we obtain 5 factorial and if we multiply first 10 natural numbers, we obtain 10 factorial.
Factorial is denoted as "!". So the product of n natural numbers is n! (read as n factorial).
For example 1 x 2 x 3 .....n = n!
For example (Reverse Order) n x (n-1) x (n-2) ..... x 3 x 2 x 1 = n!
For example 1 x 2 x 3 x 4 x 5 = 5!
For example (Reverse Order) 5 x 4 x 3 x 2 x 1 = 5!
For example 1 x 2 x 3 x 4 x 5 x 6 = 6!
For example (Reverse Order) 6 x 5 x 4 x 3 x 2 x 1 = 6!
Important factorials to remember
6! = 720
5! = 120
4! = 24
3! = 6
2! = 2
1! = 1
0! = 1
Property of Factorials
n x (n - 1)! = n!
For example if we multiply 5 with 4! [5 x 4!] or [5 x 4 x 3 x 2 x 1], we obtain 5!
For example if we multiply 6 with 5! [6 x 5!] or [6 x 5 x 4 x 3 x 2 x 1], we obtain 6!