How many paths of minimum length are there from A to B in the grid below?
The number of minimal paths is \(\displaystyle \binom{4}{1} + \binom{4}{2} + \binom{4}{3} = 14\)
![[asy] draw((3,3)--(0,0)--(3,-3));draw((5,3)--(8,0)--(5,-3));for(int i=0; i<3; i+=1){ draw((i+1,i+1)--(i+5,i-3));draw((i+1,-i-1)--(i+5,3-i));};dot((0,0)); dot((8,0));label(](/api/ssl-img-proxy?src=https%3A%2F%2Flatex.artofproblemsolving.com%2F6%2Fd%2F8%2F6d82ca1cbe4c8b4d6b508472788932c016e92ce6.png)
