the geometrical interpretation of $n!$

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We solved a $4C2$ combination, which equals $6$, which means that $4$ points forming corners of a square can be combined as a pair in $6$ ways. So what does $4!$ mean in first place geometrically. $4!=4 \cdot 3 \cdot 2 \cdot 1$. My idea is they are the number of lines possible using given points, but they contradict in cases of $0!$ and $1!$.. enlightened ye, a poor lad.. thanks