The product of first n natural numbers can be written as (n)!
(n)! = n(n-1) (n-2) .............3.2.1
thus; (n)! = n(n-1)! = n(n-1) (n-2)!
also; (0)! = 1
Fundamental Rule of Association
A. Sum Rule
Suppose A can occur in m ways and B can occur in n ways and both cannot occur simultaneously. Then A or B (at least one of them) can occur in (m+n) ways. This rule is also applicable for two or more exclusive events.
B. Product Rule
If there are m ways of doing a thing and when it has been done in any one of these m ways, then there are n ways of doing a second thing, then the total number of ways of doing two things together are m×n.