Permutations and Combinations
1.0 Factorial notation
1.0 Factorial notation
The factorial of a non-negative integer '$n$' is the product of all positive integers less than or equal to '$n$'. It is denoted as $n!$.
$$n! = (n)(n-1)(n-2)....(2)(1)$$
Here, $n \in W$ where $W$ represents set of whole numbers.
Example: $$6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$$
$$\begin{equation} \begin{aligned} n! = n(n - 1)(n - 2)...(2)(1) \\ n! = n(n - 1)! \\ {{n!} \over n} = (n - 1)! \\\end{aligned} \end{equation} $$
Special Case:
- When $n=1$, $${{1!} \over 1} = (1 - 1)!$$ which gives,$$0! = 1$$
- When $n=2$, $${{2!} \over 2} = (2 - 1)!$$which gives $$1! = 1$$
