Difference between revisions of "TDSM 5.17"
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If the ant can move without any restriction <math> \Rightarrow </math> There are <math>2^{2n}</math> posibilities it can move. | 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^{ | + | 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^{ | + | <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> |
Latest revision as of 21:39, 11 December 2017
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]
