Consider the triangular grid given below. We would like find paths from point A to point...

 

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Consider the triangular grid given below. We would like find paths from point A to point B that satisfy the following conditions. You must start at A, and end at B. At any point in between, you can either go left, right, north-west (),or north-east (7).However, when you arrive at a point from below and if you go left, you cannot go right on the same horizontal line; and if you go right, you cannot go left on the same horizontal line. A valid path is given on the grid in the middle, and a sample invalid path is given on the right. In this latter case, the path goes from D to E by going right, and then returns to F by going left on the same horizontal line, thus rendering the path invalid. B C A (a) How many distinct valid paths are there from A to B? Explain your reasoning. (b) How many valid paths pass through point C? E F Consider the triangular grid given below. We would like find paths from point A to point B that satisfy the following conditions. You must start at A, and end at B. At any point in between, you can either go left, right, north-west (),or north-east (7).However, when you arrive at a point from below and if you go left, you cannot go right on the same horizontal line; and if you go right, you cannot go left on the same horizontal line. A valid path is given on the grid in the middle, and a sample invalid path is given on the right. In this latter case, the path goes from D to E by going right, and then returns to F by going left on the same horizontal line, thus rendering the path invalid. B C A (a) How many distinct valid paths are there from A to B? Explain your reasoning. (b) How many valid paths pass through point C? E F