Aptitude Discussion

Q. |
A man positioned at the origin of the coordinate system. the man can take steps of unit measure in the direction North, East, West or South. Find the number of ways of he can reach the point $(5,6)$, covering the shortest possible distance. |

✖ A. |
252 |

✖ B. |
432 |

✔ C. |
462 |

✖ D. |
504 |

**Solution:**

Option(**C**) is correct

In order to reach $(5,6)$ covering the shortest distance at the same time the man has to make $5$ horizontal and $6$ vertical steps.

The number of ways in which these steps can be taken is given by:

$\dfrac{11!}{5!×6!}$

$= \textbf{462}$

**Name**

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Much easier*... rip would be nice to be able to edit other post. Also I had to write more to be able to post hence the babble...

**Pnr**

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Please explain the solution, why it is divides 11! by 5! and 6!

Since there are $5$ horizontal and $6$ vertical steps and their order does not matter and they are identical. So it is divided by $5!$ and $6!$.

Much earlier looking at combination of either vertical or horizontal moves. Since total number of moves will always be the sum of the 2, You can simply do 11C6, or even 11C5, since all combinations of doing it one way = total ammount since you can straight line to the finish after said moves. This can be done with any point since their sum will always be the total ammount of moves. Even point (200, 5) can be achieved in 205C5 ways which also = 205C200