Difference between revisions of "TDSM 5.17"
From The Data Science Design Manual Wikia
(Created page with "If the ants 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 <mat...") |
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| − | If the | + | If the ant can move without any restriction <math> \Rightarrow </math> There are <math>2^{2n}</math> posibilities it can move. |
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| − | <math>\Rightarrow<\math> The posibility that the ant returns to its starting points after <math>2n< | + | 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^{2n}_{n}</math> posibilities it can move. |
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| + | <math>\Rightarrow</math> The posibility that the ant returns to its starting points after <math>2n</math> steps is <math>\frac{C^{2n}_{n}}{4^n}</math> | ||
Revision as of 15:02, 8 October 2017
If the ant can move without any restriction ⇒ There are 22n posibilities it can move.
The ant returns to its starting points after 2n steps ⇒ It has to move n steps up and n steps down ⇒ There are C2nn posibilities it can move.
⇒ The posibility that the ant returns to its starting points after 2n steps is C2nn4n
