How many routes are there from the lower left corner to the upper right corner of an m*n grid if we are restricted to traveling only to the right or up? For example, in a 1*1 grid,
only two routes exist : right,up or up,right.
How many routes are there from the lower left corner to the upper right corner of an m*n grid if we are restricted to traveling only to the right or up? For example, in a 1*1 grid,
only two routes exist : right,up or up,right.
Let U stand for moving up one grid mark and R is right one.
Now to make the trip we must use m R's and n U's.
$\displaystyle \underbrace {RRR \cdots RR}_m\underbrace {UUU \cdots UU}_n$, how many ways can we rearrange that string?
Let U stand for moving up one grid mark and R is right one.
Now to make the trip we must use m R's and n U's.
$\displaystyle \underbrace {RRR \cdots RR}_m\underbrace {UUU \cdots UU}_n$, how many ways can we rearrange that string?