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# counting

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How do I solve this

Find the number of paths from A to I, if each step must be in a right-ward direction.  (For example, one possible path is A C D E F G H I)

Mar 19, 2023

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Based on the information given, we can represent the grid as follows:

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A-B-C-D-E-F-G-H-I

Since each step must be in a rightward direction, the only possible paths are those that go from left to right across the grid. We can count the number of such paths by counting the number of ways to choose the steps from the available options.

Starting at A, we have only one option: to step to B. From B, we have two options: we can either step to C or we can step directly to D. From each subsequent node, we have two options: we can either stay on the same row and move to the next column, or we can move diagonally up to the next row and then move to the next column. Using this method, we can count the total number of paths from A to I as follows:

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A -> B -> C -> D -> E -> F -> G -> H -> I 1 2 2 4 4 8 8 16 16

Therefore, there are 16 possible paths from A to I, if each step must be in a rightward direction.

Mar 19, 2023