Write legibly and neatly. You do NOT need to simplify any numerical answers; you

Question

Write legibly and neatly. You do NOT need to simplify any numerical answers; you can leave your answers in terms of factorials and binomial coefficients. You may show your work for partial credit, ut if you think the answer is obvious then you don't need to show work. (1) You are walking on points in the plane with integer coordinates. Each time you can move either one unit down or one unit right; for example, from (3, 7) you can move either to (3,6) or (4, 7). You start at the point (0, 8) and want to reach (12,0). How many possible routes do you have?

Explanation / Answer

Starting point is (0,8) and we need to reach (12,0)

first coordinate can only be changed by right moves and second only by down moves

So we have a total of 8 down moves and 12 right moves which are independent of each other because down only affects second coordinate and rihgt only the first

So we have 12*8=96 possible paths

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