Permutation of the grids: If an Imaginary square shaped city has 9 horizontal streets and 16 vertical streets, A and B are the 2 diagonal points of the city, if I want to go from point A to point B, where all the streets which form this imaginary grid have distinct names, in how many ways can I walk from point A to B moving through different pathways? It is necessary to note that one has to choose the shortest paths, meaning that going opposite to the direction of destination is prohibited, However one is allowed all other freedoms like continuing on a horizontal or a vertical street till the edge of the grid city and so on and so forth.
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Welcome to stackexchange. You are more likely to get help rather than downvotes or votes to close if you edit the question to show us what you have tried and where you are stuck. Are you allowed to double back? Does going several blocks in the same direction count as a different route? Can you solve the problem for a small city? – Ethan Bolker Apr 09 '18 at 17:28
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Probably a duplicate: https://math.stackexchange.com/questions/636128/calculating-the-number-of-possible-paths-through-some-squares, https://math.stackexchange.com/questions/321192/lattice-paths-and-catalan-numbers – Ethan Bolker Apr 09 '18 at 17:40
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No Mr. Bolker, the route is the permutation of all the possible pathways, so it is futile to recount the same path unless one is changing the combination to attain the destination, for the streets are distinct, for counting the number of ways, use of blocks would futile (from my point of view), because we are asked the possible pathways and not street segments we need for attaining the goal. – Hrishikesh patel Apr 09 '18 at 17:42