Consider a city whose streets are laid out as a grid. Streets run north-south or east-west. A visitor is dropped off by a cab at a certain intersection and would like to visit a museum that is 6 blocks to the east and 3 blocks to the north of his current location. The visitor always takes a direct path and never travels west or south in the course of his walk. How many distinct paths are there for the visitor to walk to the museum

84 possible paths

Step-by-step explanation:

Given

--- 3 blocks north

--- 6 blocks east

Required

Number of distinct path

To solve this question, we make use of the following formula

The above formula implies that;

On a single path, there is a total of m + n steps to get to a particular position, where each path is either in m direction or n direction.

In this case:

So, we have:

Apply combination formula

Expand the numerator

Expand the denominator

Hence, there are 84 possible paths

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