Consider the grid NxN of pairs of integers. Suppose that one starts at the origin A=(0,0) and moves to the point B=(-2,10) in 10 steps. Each step is composed of either an "Up" movement ((i,j) -- (i+1,j+1)) or an "Down" movement ((i,j) -- (i-1,j+1)). The total number of distinct paths that are composed of "Up" and "Down" movements is....

Question

Consider the grid NxN of pairs of integers. Suppose that one starts at the origin A=(0,0) and moves to the point B=(-2,10) in 10 steps. Each step is composed of either an "Up" movement ((i,j) --> (i+1,j+1)) or an "Down" movement ((i,j) --> (i-1,j+1)). The total number of distinct paths that are composed of "Up" and "Down" movements is....

anonymous · Answer

thats 6 down moves and 4 up moves, making it 10!/(6! *4!), correct?

anonymous · Answer

answer is 210?