**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!**