Question

How many different paths are there between the node in the lower left corner and the node in

the upper right corner of a square mesh with n nodes in each row and column? Justify your answer.

Answer 1

Solution for the problem is provided below, please comment if any doubts:

Answer:

Explanation:

The given problem is to find the number of roots between lower left corner and the upper right corner node.

Each side has “n” nodes thus each side has “n-1” edges.

Thus the shortest distance between the given source and destination is “2*(n-1)”.

Now to reach from lower left to upper right, we need to follow two directions, either right or up, it is clear that we need to take “n-1” right steps and “n-1” up steps.

Now in the “2*(n-1)” length paths there should be “n-1” right and “n-1” up moves.

The number of possible combination of such nodes is: