Just wanted to share a nice problem.I have given my method below.More answers are welcome.
Consider a rectangular integral grid of size $m*n$.A person has to travel from one end say $(0,0)$ to the diagonally opposite end $(m,n)$.He moves one step at a time towards the east or towards the north(that is,never moves towards the west or south at any time).How many distinct paths exist from the point A to the point C ?
$\endgroup$1 Answer
$\begingroup$Suppose you had to describe this path to a person who cannot see the figure,you could tell him in form of a string say: $EENENEENN$.
This string we just formed helps to realize all possible paths from one vertex to the diagonally opposite vetex. (E stands for EAST and N stands for NORTH)
$\endgroup$ 1So we just have to find all permutations of the string which is $\frac{(m+n)!}{m!n!}$ .
