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....

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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....

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thats 6 down moves and 4 up moves, making it 10!/(6! *4!), correct?
answer is 210?

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