Question

Starting at the point (0,0) how many ways are there to get to the point (7,4) if you have to pass through the point (2,2) and each step can only be in a positive direction. (i.e. to the right or up)?

Answer 1

The number of ways there are to get to the point (7,4) if you have to pass through the point (2,2) is; 1266 ways

How to find the lattice Paths?

The formula to get the number of ways to get to the lattice point (x, y) (supposing x, y ≥ 0) by taking steps of one unit each either in the eastward or northward direction is exactly;

(x + y)

          = (x + y)!/(x!y!)

(   x   )

Thus, number of ways from (0, 0) to (2, 2) = (2 + 2)!/(2!2!) = 6 ways

Number of ways to get to point (7,4) from (2, 2) is;

((7 - 2) + (4 - 2))!/(2!2!) = 7!/(2!2!) = 1260

Thus, total number of ways = 1266 ways

Read more about Lattice paths at; brainly.com/question/2109763

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