TDSM 5.17
From The Data Science Design Manual Wikia
If the ant can move without any restriction [math] \Rightarrow [/math] There are [math]2^{2n}[/math] posibilities it can move.
The ant returns to its starting points after [math]2n[/math] steps [math]\Rightarrow[/math] It has to move [math]n[/math] steps up and [math]n[/math] steps down [math]\Rightarrow[/math] There are [math]C^{n}_{2n}[/math] posibilities it can move.
[math]\Rightarrow[/math] The posibility that the ant returns to its starting points after [math]2n[/math] steps is [math]\frac{C^{n}_{2n}}{4^n}[/math]
