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The factorial symbol ! is placed after a positive integer to indicate that it should be multiplied by every whole number less than it, through $$1$$. For example:
$$6!=6·5·4·3·2·1$$

The factorial operation, denoted as n!, states that:
$$n!=n\left(n–1\right)\left(n–2\right)\left(n–3\right)···3·2·1$$

The factorial operation is often used to mathematically express combinations, different ways that selected elements can be arranged when the order does not matter, and permutations, different ways that selected elements can be arranged when the order does matter.

The factorial of $$0$$ is $$1$$.
$$0!=1$$